Relevant bibliographies by topics / Non-Selfadjoint operator

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  2. Dissertations / Theses
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  4. Book chapters
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Academic literature on the topic 'Non-Selfadjoint operator'

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Published: 3 June 2023

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Journal articles on the topic "Non-Selfadjoint operator"

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Kukushkin, M. V. "Замечание о спектральной теореме для неограниченных несамосопряженных операторов." Вестник КРАУНЦ. Физико-математические науки, no. 2 (September 25, 2022): 42–61. http://dx.doi.org/10.26117/2079-6641-2022-39-2-42-61.

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In this paper, we deal with non-selfadjoint operators with the compact resolvent. Having been inspired by the Lidskii idea involving a notion of convergence of a series on the root vectors of the operator in a weaker – Abel-Lidskii sense, we proceed constructing theory in the direction. The main concept of the paper is a generalization of the spectral theorem for a non-selfadjoint operator. In this way, we come to the definition of the operator function of an unbounded non-selfadjoint operator. As an application, we notice some approaches allowing us to principally broaden conditions imposed on the right-hand side of the evolution equation in the abstract Hilbert space. В данной работе, дав определение сходимости ряда по корневым векторам в смысле Абеля-Лидского, мы представляем актуальное приложение в теории эволюционных уравнений. Основной целью является подход, позволяющий нам принципиально расширить условия, налагаемые на правую часть эволюционного уравнения в абстрактном гильбертовом пространстве. Таким образом, мы приходим копределению функции неограниченного не самосопряженно- го оператора. Между тем, мы вовлекаем дополнительную концепцию, которая является обобщением спектральной теоремы для не самосопряженного оператора.
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Donsig, Allan P., and S. C. Power. "The Failure of Approximate Inner Conjugacy for Standard Diagonals in Regular Limit Algebras." Canadian Mathematical Bulletin 39, no. 4 (December 1, 1996): 420–28. http://dx.doi.org/10.4153/cmb-1996-050-5.

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AbstractAF C*-algebras contain natural AF masas which, here, we call standard diagonals. Standard diagonals are unique, in the sense that two standard diagonals in an AF C*-algebra are conjugate by an approximately inner automorphism. We show that this uniqueness fails for non-selfadjoint AF operator algebras. Precisely, we construct two standard diagonals in a particular non-selfadjoint AF operator algebra which are not conjugate by an approximately inner automorphism of the non-selfadjoint algebra.
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Pelloni, B., and D. A. Smith. "Spectral theory of some non-selfadjoint linear differential operators." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2154 (June 8, 2013): 20130019. http://dx.doi.org/10.1098/rspa.2013.0019.

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We give a characterization of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator S with the properties of the solution of a corresponding boundary value problem for the partial differential equation ∂ t q ±i Sq =0. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular, whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.
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Kukushkin, Maksim V. "On One Method of Studying Spectral Properties of Non-selfadjoint Operators." Abstract and Applied Analysis 2020 (September 1, 2020): 1–13. http://dx.doi.org/10.1155/2020/1461647.

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In this paper, we explore a certain class of Non-selfadjoint operators acting on a complex separable Hilbert space. We consider a perturbation of a nonselfadjoint operator by an operator that is also nonselfadjoint. Our consideration is based on known spectral properties of the real component of a nonselfadjoint compact operator. Using a technique of the sesquilinear forms theory, we establish the compactness property of the resolvent and obtain the asymptotic equivalence between the real component of the resolvent and the resolvent of the real component for some class of nonselfadjoint operators. We obtain a classification of nonselfadjoint operators in accordance with belonging their resolvent to the Schatten-von Neumann class and formulate a sufficient condition of completeness of the root vector system. Finally, we obtain an asymptotic formula for the eigenvalues.
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Dong, Aiju, and Chengjun Hou. "On some maximal non-selfadjoint operator algebras." Expositiones Mathematicae 30, no. 3 (2012): 309–17. http://dx.doi.org/10.1016/j.exmath.2012.08.001.

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Zhao, Junxi. "On invertibility in non-selfadjoint operator algebras." Proceedings of the American Mathematical Society 125, no. 1 (1997): 101–9. http://dx.doi.org/10.1090/s0002-9939-97-03645-9.

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Holubová, G., and P. Nečesal. "Nontrivial Fučík spectrum of one non-selfadjoint operator." Nonlinear Analysis: Theory, Methods & Applications 69, no. 9 (November 2008): 2930–41. http://dx.doi.org/10.1016/j.na.2007.08.066.

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Ryzhov, Vladimir. "Functional Model of a Closed Non-Selfadjoint Operator." Integral Equations and Operator Theory 60, no. 4 (March 13, 2008): 539–71. http://dx.doi.org/10.1007/s00020-008-1574-9.

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Hou, Chengjun, and Cuiping Wei. "Completely bounded cohomology of non-selfadjoint operator algebras." Acta Mathematica Scientia 27, no. 1 (January 2007): 25–33. http://dx.doi.org/10.1016/s0252-9602(07)60003-4.

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Bairamov, E., E. K. Arpat, and G. Mutlu. "Spectral properties of non-selfadjoint Sturm–Liouville operator with operator coefficient." Journal of Mathematical Analysis and Applications 456, no. 1 (December 2017): 293–306. http://dx.doi.org/10.1016/j.jmaa.2017.07.001.

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Dissertations / Theses on the topic "Non-Selfadjoint operator"

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Torshage, Axel. "Non-selfadjoint operator functions." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-143085.

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Spectral properties of linear operators and operator functions can be used to analyze models in nature. When dispersion and damping are taken into account, the dependence of the spectral parameter is in general non-linear and the operators are not selfadjoint. In this thesis non-selfadjoint operator functions are studied and several methods for obtaining properties of unbounded non-selfadjoint operator functions are presented. Equivalence is used to characterize operator functions since two equivalent operators share many significant characteristics such as the spectrum and closeness. Methods of linearization and other types of equivalences are presented for a class of unbounded operator matrix functions. To study properties of the spectrum for non-selfadjoint operator functions, the numerical range is a powerful tool. The thesis introduces an optimal enclosure of the numerical range of a class of unbounded operator functions. The new enclosure can be computed explicitly, and it is investigated in detail. Many properties of the numerical range such as the number of components can be deduced from the enclosure. Furthermore, it is utilized to prove the existence of an infinite number of eigenvalues accumulating to specific points in the complex plane. Among the results are proofs of accumulation of eigenvalues to the singularities of a class of unbounded rational operator functions. The enclosure of the numerical range is also used to find optimal and computable estimates of the norm of resolvent and a corresponding enclosure of the ε-pseudospectrum.
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Kastis, Eleftherios Michail. "Non-selfadjoint operator algebras generated by unitary semigroups." Thesis, Lancaster University, 2017. http://eprints.lancs.ac.uk/88135/.

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The parabolic algebra was introduced by Katavolos and Power, in 1997, as the weak∗-closed operator algebra acting on L2(R) that is generated by the translation and multiplication semigroups. In particular, they proved that this algebra is reflexive, in the sense of Halmos, and is equal to the Fourier binest algebra, that is, to the algebra of operators that leave invariant the subspaces in the Volterra nest and its analytic counterpart. We prove that a similar result holds for the corresponding algebras acting on Lp(R), where 1 < p < ∞. It is also shown that the reflexive closures of the Fourier binests on Lp(R) are all order isomorphic for 1 < p < ∞. The weakly closed operator algebra on L2(R) generated by the one-parameter semigroups for translation, dilation and multiplication by eiλx, λ ≥ 0, is shown to be a reflexive operator algebra with invariant subspace lattice equal to a binest. This triple semigroup algebra, Aph, is antisymmetric, it has a nonzero proper weakly closed ideal generated by the finite-rank operators, and its unitary automorphism group is R. Furthermore, the 8 choices of semigroup triples provide 2 unitary equivalence classes of operator algebras, with Aph and (Aph)∗ being chiral representatives. In chapter 4, we consider analogous operator norm closed semigroup algebras. Namely, we identify the norm closed parabolic algebra Ap with a semicrossed product for the action on analytic almost periodic functions by the semigroup of one-sided translations and we determine its isometric isomorphism group. Moreover, it is shown that the norm closed triple semigroup algebra AphG+ is the triple semi-crossed product Ap ×v G+, where v denotes the action of one-sided dilations. The structure of isometric automorphisms of AphG+ is determined and AphG+ is shown to be chiral with respect to isometric isomorphisms. Finally, we consider further results and state open questions. Namely, we show that the quasicompact algebra QAp of the parabolic algebra is strictly larger than the algebra CI + K(H), and give a new proof of reflexivity of certain operator algebras,generated by the image of the left regular representation of the Heisenberg semigroup H+.
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Nath, Jiban Kumar. "Spectral theory of non-selfadjoint operators." Thesis, King's College London (University of London), 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.271218.

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Saboormaleki, Mahmood. "Spectral analysis of non-selfadjoint differential operators." Thesis, Sheffield Hallam University, 1998. http://shura.shu.ac.uk/20306/.

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This thesis is concerned with the extension of classical Titchmarsh-Weyl theory to non-selfadjoint Sturm-Liouville operators on the half-line. We introduce the thesis with some mathematical background which is needed for the development of the main results. This includes a brief summary of relevant aspects of Lebesgue measure and integration, analytic function theory, unbounded operator theory, and selfadjoint extensions of symmetric operators, and is given in the first two chapters. An introduction to Weyl theory and related topics for the self adjoint case can be found in Chapter 3. The main work on non-selfadjoint second order differential operators associated with the equation y" + qy = lambday begins in Chapter 4. We first describe Sims' extension of Weyl's limit point, limit circle theory to the non-selfadjoint case, and some later generalisations by McLeod. Some standard results of Titchmarsh are then extended from the selfadjoint to the non-selfadjoint case and an important result on the stability of the essential spectrum of a non-selfadjoint differential equation of form (py')'+qy =lambday is also obtained. In Chapter 5, we extend some results of Chaudhuri-Everitt to non-selfadjoint operators in which the potential satisfies the condition lim[x]infinityq(x) = L. Some worked examples at the end of Chapter 5 show that in certain cases where there is a complex boundary condition and real coefficient, or a complex coefficient with real boundary condition, some complex eigenvalues can be explicitly calculated. Finally in Chapter 6 we describe a physical problem which gives rise to a non-selfadjoint eigenvalue problem on the half-line. Keywords: Differential operator, Non-selfadjoint, Spectrum, Eigenvalue problem, Weyl m-function.
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CAVALCANTI, ANDRE ZACCUR UCHOA. "RESULTS OF AMBROSETTI-PRODI TYPE FOR NON-SELFADJOINT ELLIPTIC OPERATORS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=33600@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
O célebre teorema de Ambrosetti-Prodi estuda perturbações do Laplaciano sob condições de Dirichlet por funções não lineares que saltam sobre o autovalor principal do operador. Diversas extensões desse resultado foram obtidos para operadores auto-adjuntos, em particular por Berger-Podolak em 1975, que deram uma descrição geométrica do conjunto solução. Nós empregamos técnicas baseadas no princípio do máximo que nos permite obter novos resultados inclusive para o cenário auto-adjunto. Em particular, nós mostramos que o operador semi-linear é uma dobra global. Obtemos também uma contagem exata de soluções para esses operadores ainda quando a perturbação não é suave.
The celebrated Ambrosetti-Prodi theorem studies perturbations of the Dirichlet Laplacian by a nonlinear function jumping over the principal eigenvalue of the operator. Various extensions of this landmark result were obtained for self-adjoint operators, in particular by Berger-Podolak in 1975, who gave a geometrical description of the solution set. In this thesis we show that similar theorems are valid for non self-adjoint operators. We employ techniques based on the maximum principle, which even let us obtain new results in the self-adjoint setting. In particular, we show that the semilinear operator is a fold. As a consequence, we obtain exact count of solutions for these operators even when the perturbation is non-smooth.
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Al, Sheikh Lamis. "Scattering resonances and Pseudospectrum : stability and completeness aspects in optical and gravitational systems." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2022. http://www.theses.fr/2022UBFCK007.

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Le contexte général de cette thèse est un effort pour établir un pont entre la physique gravitationnelle et optique, spécifiquement dans le contexte des problèmes de diffusion à l’aide des concepts et des outils tirés de la théorie des opérateurs non auto-adjoints. Nous nous concentrons sur les modes quasi-normaux (MQN), appelés les modes de résonance naturels des structures à fuites ouvertes sous des perturbations linéaires soumises à des conditions de bords sortantes.Ils sont également appelés résonances de diffusion. Dans le cas auto-adjoint conservateur, le théorème spectral garantit la complétude et la stabilité spectrale des modes normaux associés.En ce sens, une question naturelle dans le cadre de non auto-adjoint est reliée à la caractérisation et à l’évaluation des notions appropriées de complétude de MQNs et de stabilité spectrale dans les systèmes ouverts non conservateurs. Ceci définit les objectifs de cette thèse. Pour ce faire, et contrairement à l’approche traditionnelle des résonances de diffusion, nous adoptons une méthodologie dans laquelle les MQNs sont présentés comme un problème spectral d’un opérateur approprié non auto-adjoint. Plus précisément, cette méthodologie est basée sur les trois ingrédients suivants :(i) L’approche hyperboloïdale: L’approche en tranchant hyperboloïdales est déjà utilisée dansles problèmes gravitationnels, nous l’avons introduite dans les problèmes optiques. L’idéeest d’étudier l’équation d’onde en tranches hyperboliques au lieu des tranches de Cauchy habituellement utilisées. Le système de coordonnées est plus adapté à la problématique des QNMs et de ses conditions aux limites sortantes, en particulier, aborder les modes explosifs dans l’approche de Cauchy. Les modes sont normalisables en de telles coordonnées ettravailler dans ces tranches éliminent le besoin d’imposer les conditions de bords sortantes.(ii) Pseudospectre d’un opérateur: la notion de epsilon-pseudospectre permet d’évaluer la (in)stabilité des valeurs propres d’un opérateur dans le plan complexe en raison d’une perturbation de l’opérateur d’ordre epsilon. Cette thèse introduit la notion de pseudospectre en physique gravitationnel et optique au voisinage des valeurs propres.(iii) Au niveau technique, les méthodes spectrales fournissent un outil efficace pour traduirele problème en un problème numérique. En particulier, nous avons utilisé la base de Chebyshev pour l’expansion des nos champs. Les résultats de ce travail touchent trois domaines :(i) L’instabilité des MQN pour certaines classes de potentiels. Les modes fondamentaux sont stables spécialement sous de petites perturbations "à haute fréquence", alors que les harmoniques sont sensibles à de telles perturbations. L’instabilité des harmoniques augmente à mesure que leur partie imaginaire grandit.(ii) L’universalité du comportement asymptotique des MQNs et du pseudospectre. Nous remarquons un comportement asymptotiquement logarithmique des lignes de contour du pseudospectre et délimitant les branches d’ouverture des MQNs par le bas.(iii) MQNs expansion. Nous revisitons les expansions résonantes asymptotiques de Lax &Phillips d’un "champ diffusé" en termes de MQNs pour nos problèmes physiques. En particulier, nous utilisons le développement de Keldysh des généralisations des expressions pour les modes normaux des systèmes conservateurs, spécifiquement en termes de fonctions propres MQN normalisables et d’expressions explicites pour les coefficients d’excitation
The general context of this thesis is an effort to establish a bridge between gravitational andoptical physics, specifically in the context of scattering problems using as a guideline concepts andtools taken from the theory of non-self-adjoint operators. Our focus is on Quasi-Normal Modes(QNMs), namely the natural resonant modes of open leaky structures under linear perturbationssubject to outgoing boundary conditions. They also are referred to as scattering resonances.In the conservative self-adjoint case the spectral theorem guarantees the completeness andspectral stability of the associated normal modes. In this sense, a natural question in the non-self-adjoint setting refers to the characterization and assessment of appropriate notions of QNMcompleteness and spectral stability in open non-conservative systems. This defines the generalobjective of this thesis. To this aim, and in contrast with the traditional approach to scatter-ing resonances, we adopt a methodology in which QNMs are cast as a spectral problem of anappropriate non-self-adjoint operator. Specifically this methodology is based on following threeingredients:(i) Hyperboloidal approach: The hyperboloidal slicing approach is already used in gravitationalproblems, we introduced it here to optical ones. The idea is to study the wave equationin hyperbolic slices instead of usually used Cauchy slices. The system of coordinates ismore adapted to the problem of QNMs and its outgoing boundary conditions, in particularaddressing the exploding modes in the Cauchy approach. The modes are normalizable insuch coordinates and working in these slices eliminate the need of imposing the outgoingboundary conditions.(ii) Pseudospectrum of an operator: the notion of epsilon-pseudospectrum allows to assess the (in)stabilityof eigenvalues of an operator in the complex plane due to a perturbation to the operator oforder epsilon. This thesis introduces the notion of pseudospectrum in gravitational and opticalphysics in the vicinity of the eigenvalues.(iii) Numerical Chebyshev spectral methods: On the technical level, spectral methods providesan efficient tool when translating the problem into a numerical one. In particular we usedChebyshev basis to expand our fields.The results of this work touch three areas:(i) The instability of QNMs for some class of potentials. The fundamental modes are stablespecially under small "high frequency" perturbations, whereas overtones are sensitive tosuch perturbations. The instability of the overtones increases as their imaginary part grows.(ii) The universality of the asymptotic behaviour of QNMs and pseudospectrum. We remarkan asymptotically logarithmic behavior of pseudospectrum contour lines and bounding theopening QNMs branches from below.(iii) QNMs expansion. We revisit Lax & Phillips asymptotic resonant expansions of a "scattered field" in terms of QNMs in our physical settings. In particular , we make use of Keldysh expansion of the generalizations of the expressions for normal modes of conservative systems, specifically in terms of normalizable QNM eigenfunctions and explicit expressions for the excitation coefficients
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Henry, Raphaël. "Spectre et pseudospectre d'opérateurs non-autoadjoints." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00924425.

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L'instabilité du spectre des opérateurs non-autoadjoints constitue la thématique centrale de cette thèse. Notre premier objectif est de mettre en évidence ce phénomène dans le cas de certains modèles naturels tels que l'opérateur d'Airy, l'oscillateur harmonique ou l'oscillateur cubique complexes. Dans ce but, nous nous intéressons au comportement des projecteurs spectraux associés aux valeurs propres de ces opérateurs, poursuivant une démarche initiée par E. B. Davies. Le second objectif de notre travail consiste à montrer de quelle manière ces modèles peuvent contribuer à la compréhension de certains problèmes issus de domaines mathématiques et physiques aussi variés que la mécanique quantique, la supraconductivité ou la théorie du contrôle. Nos résultats sur l'instabilité spectrale de l'oscillateur cubique complexe viennent ainsi corroborer un travail de B. Krejcirik et P. Siegl, soulignant l'impossibilité de fournir une justification rigoureuse aux théories actuelles de la mécanique quantique non-hermitienne. Par ailleurs, nous nous appuyons sur les propriétés des modèles mentionnés ci-dessus pour obtenir des résultats sur le spectre et la résolvante d'opérateurs de Schrödinger à potentiels imaginaires purs dans des ouverts bornés. Ces résultats peuvent en particulier être appliqués à l'étude du système de Ginzburg-Landau dépendant du temps en supraconductivité. Enfin, nous présentons des résultats sur la contrôlabilité d'équations paraboliques dégénérées qui reposent sur une étude spectrale et pseudospectrale de l'opérateur d'Airy et de l'oscillateur harmonique complexes. Ce dernier travail est le fruit d'une collaboration avec K. Beauchard, B. Helffer et L. Robbiano.
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Alphonse, Paul. "Régularité des solutions et contrôlabilité d'équations d'évolution associées à des opérateursnon-autoadjoints." Thesis, Rennes 1, 2020. http://www.theses.fr/2020REN1S003.

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Le sujet de cette thèse a trait à l'étude microlocale fine des propriétés de régularisation et de décroissance des équations d'évolution associées à deux classes d'opérateurs non-autoadjoints avec des applications à l’étude de leurs propriétés sous-elliptiques et à la contrôlabilité à zéro de ces mêmes équations. La première classe est constituée d'opérateurs non-locaux donnés par les opérateurs d'Ornstein-Uhlenbeck fractionnaires qui apparaissent comme la somme d'une diffusion fractionnaire et d'un opérateur de transport linéaire. La deuxième classe est celle des opérateursdifférentiels quadratiques accrétifs donnés par la quantification de Weyl de formes quadratiques définies sur l'espace des phases, à valeurs complexes et de parties réelles positives. L'objectif de ce travail est de comprendre comment les possibles phénomènes de non-commutation entre les parties autoadjointe et anti-autoadjointe de ces opérateurs permettent aux semi-groupes qu'ils engendrent de jouir de propriétés de régularisation et de décroissance dans certaines directions spécifiques de l'espace des phases que l'on décrit explicitement
The subject of this thesis deals with the sharp microlocal study of the smoothing and decreasing properties of evolution equations associated with two classes of non-selfadjoint operators with applications to the study of their subelliptic properties and to the null-controllability of these equations. The first class is composed of non-local operators given by the Ornstein-Uhlenbeck operators defined as the sum of a fractional diffusion and a linear transport operator. The second class is the class of accretive quadratic differential operators given by the Weyl quantization of complex-valued quadratic forms defined on the phase space with non-negative real parts. The aim of this work is to understand how the possible non-commutation phenomena between the self-adjoint and the skew-selfadjoint parts of these operators allow the associated semigroups to enjoy smoothing and decreasing properties in specific directions of the phase space that are explicitly described
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Ramsey, Christopher. "Maximal ideal space techniques in non-selfadjoint operator algebras." Thesis, 2013. http://hdl.handle.net/10012/7464.

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The following thesis is divided into two main parts. In the first part we study the problem of characterizing algebras of functions living on analytic varieties. Specifically, we consider the restrictions M_V of the multiplier algebra M of Drury-Arveson space to a holomorphic subvariety V of the unit ball as well as the algebras A_V of continuous multipliers under the same restriction. We find that M_V is completely isometrically isomorphic to cM_W if and only if W is the image of V under a biholomorphic automorphism of the ball. In this case, the isomorphism is unitarily implemented. Furthermore, when V and W are homogeneous varieties then A_V is isometrically isomorphic to A_W if and only if the defining polynomial relations are the same up to a change of variables. The problem of characterizing when two such algebras are (algebraically) isomorphic is also studied. In the continuous homogeneous case, two algebras are isomorphic if and only if they are similar. However, in the multiplier algebra case the problem is much harder and several examples will be given where no such characterization is possible. In the second part we study the triangular subalgebras of UHF algebras which provide new examples of algebras with the Dirichlet property and the Ando property. This in turn allows us to describe the semicrossed product by an isometric automorphism. We also study the isometric automorphism group of these algebras and prove that it decomposes into the semidirect product of an abelian group by a torsion free group. Various other structure results are proven as well.
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Hansmann, Marcel. "Eigenvalues of compactly perturbed linear operators." 2018. https://monarch.qucosa.de/id/qucosa%3A23447.

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This cumulative habilitation thesis is concerned with eigenvalues of compactly perturbed operators in Banach and Hilbert spaces. A general theory for studying such eigenvalues is developed and applied to the study of some concrete operators of mathematical physics.
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Books on the topic "Non-Selfadjoint operator"

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Metrics on the phase space and non-selfadjoint pseudo-differential operators. Basel: Birkhäuser, 2010.

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Bagarello, Fabio, Jean Pierre Gazeau, Franciszek Hugon Szafraniec, and Miloslav Znojil, eds. Non-Selfadjoint Operators in Quantum Physics. Hoboken, NJ, USA: John Wiley & Sons, Inc, 2015. http://dx.doi.org/10.1002/9781118855300.

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Lerner, Nicolas. Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-8510-1.

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Christensen, Jens Gerlach. Trends in harmonic analysis and its applications: AMS special session on harmonic analysis and its applications : March 29-30, 2014, University of Maryland, Baltimore County, Baltimore, MD. Providence, Rhode Island: American Mathematical Society, 2015.

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Agranovich, M. S. Non-selfadjoint Elliptic Operators. Springer-Verlag, 2007.

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Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects. Wiley, 2015.

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Gazeau, Jean-Pierre, Fabio Bagarello, Franciszek Hugon Szafraniec, and Miloslav Znojil. Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects. Wiley & Sons, Incorporated, John, 2015.

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Gazeau, Jean-Pierre, Fabio Bagarello, Franciszek Hugon Szafraniec, and Miloslav Znojil. Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects. Wiley & Sons, Limited, John, 2015.

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Gazeau, Jean-Pierre, Fabio Bagarello, Franciszek Hugon Szafraniec, and Miloslav Znojil. Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects. Wiley & Sons, Incorporated, John, 2015.

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Zolotarev, V. A. Analytic Methods of Spectral Representations of Non- Selfadjoint (Non-Unitary) Operators. PH “Akademperiodyka”, 2020. http://dx.doi.org/10.15407/akademperiodika.421.433.

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This book is concerned with model representations theory of linear non- selfadjoint and non-unitary operators, one of booming areas of functional analysis. This area owes its origin to fundamental works by M.S. Livˇsic on the theory of characteristic functions, deep studies of B.S.-Nagy and C. Foias on the dilation theory, and also to the Lax—Phillips scattering theory. A uni- form conceptual approach organically uniting all these research areas in the theory of non-selfadjoint and non-unitary operators is developed in this book. New analytic methods that allow solving some important problems from the theory of spectral representations in this area of analysis are also presented in this book. The book is aimed at the specialists working in this area of analysis and is accessible to senior math students of universities.
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Book chapters on the topic "Non-Selfadjoint operator"

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Sakhnovich, L. "Weyl-Titchmarsh Matrix Functions and Spectrum of Non-selfadjoint Dirac Type Equation." In Current Trends in Operator Theory and its Applications, 539–51. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0348-7881-4_24.

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Artamonov, Nikita. "Exponential Decay of Semigroups for Second-order Non-selfadjoint Linear Differential Equations." In Recent Progress in Operator Theory and Its Applications, 1–10. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0346-5_1.

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Sakhnovich, Alexander L. "GBDT of discrete skew-selfadjoint Dirac systems and explicit solutions of the corresponding non-stationary problems." In Operator Theory, Analysis and the State Space Approach, 389–98. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04269-1_15.

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Seifert, Christian, Sascha Trostorff, and Marcus Waurick. "Evolutionary Inclusions." In Evolutionary Equations, 275–97. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89397-2_17.

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AbstractThis chapter is devoted to the study of evolutionary inclusions. In contrast to evolutionary equations, we will replace the skew-selfadjoint operator A by a so-called maximal monotone relation A ⊆ H × H in the Hilbert space H. The resulting problem is then no longer an equation, but just an inclusion; that is, we consider problems of the form $$\displaystyle (u,f)\in \overline {\partial _{t,\nu }M(\partial _{t,\nu })+A}, $$ ( u , f ) ∈ ∂ t , ν M ( ∂ t , ν ) + A ¯ , where $$f\in L_{2,\nu }(\mathbb {R};H)$$ f ∈ L 2 , ν ( ℝ ; H ) is given and $$u\in L_{2,\nu }(\mathbb {R};H)$$ u ∈ L 2 , ν ( ℝ ; H ) is to be determined. This generalisation allows the treatment of certain non-linear problems, since we will not require any linearity for the relation A. Moreover, the property that A is just a relation and not neccessarily an operator can be used to treat hysteresis phenomena, which for instance occur in the theory of elasticity and electro-magnetism.
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Lerner, Nicolas. "Estimates for Non-Selfadjoint Operators." In Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators, 161–286. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-8510-1_3.

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Bagarello, F., J. P. Gazeau, F. Szafraniec, and M. Znojil. "Introduction." In Non-Selfadjoint Operators in Quantum Physics, 1–6. Hoboken, NJ, USA: John Wiley & Sons, Inc, 2015. http://dx.doi.org/10.1002/9781118855300.ch0.

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Znojil, Miloslav. "Non-self-adjoint operators in quantum physics: ideas, people, and trends." In Non-Selfadjoint Operators in Quantum Physics, 7–58. Hoboken, NJ, USA: John Wiley & Sons, Inc, 2015. http://dx.doi.org/10.1002/9781118855300.ch1.

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Szafraniec, Franciszek Hugon. "Operators of the quantum harmonic oscillator and its relatives." In Non-Selfadjoint Operators in Quantum Physics, 59–120. Hoboken, NJ, USA: John Wiley & Sons, Inc, 2015. http://dx.doi.org/10.1002/9781118855300.ch2.

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Bagarello, Fabio. "Deformed Canonical (anti-)commutation relations and non-self-adjoint hamiltonians." In Non-Selfadjoint Operators in Quantum Physics, 121–88. Hoboken, NJ, USA: John Wiley & Sons, Inc, 2015. http://dx.doi.org/10.1002/9781118855300.ch3.

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Caliceti, Emanuela, and Sandro Graffi. "Moyal brackets and the Weyl quantization." In Non-Selfadjoint Operators in Quantum Physics, 189–240. Hoboken, NJ, USA: John Wiley & Sons, Inc, 2015. http://dx.doi.org/10.1002/9781118855300.ch4.

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Conference papers on the topic "Non-Selfadjoint operator"

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Kirillov, Oleg N., and Alexander P. Seyranian. "Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems." In ASME 2002 21st International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/omae2002-28076.

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In the present paper eigenvalue problems for non-selfadjoint linear differential operators smoothly dependent on a vector of real parameters are considered. Bifurcation of eigenvalues along smooth curves in the parameter space is studied. The case of multipleeigen value with Keldysh chain of arbitrary length is considered. Explicit expressions describing bifurcation of eigen-values are found. The obtained formulae use eigenfunctions and associated functions of the adjoint eigenvalue problems as well as the derivatives of the differential operator taken at the initial point of the parameter space. These results are important for the stability theory, sensitivity analysis and structural optimization. As a mechanical application the extended Beck’s problem of stability of an elastic column under action of potential force and tangential follower force is considered and discussed in detail.
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