Relevant bibliographies by topics / Self-adjoint operator

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Self-adjoint operator'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 June 2025

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Journal articles on the topic "Self-adjoint operator"

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Araujo, Vanilse S., F. A. B. Coutinho, and J. Fernando Perez. "Operator domains and self-adjoint operators." American Journal of Physics 72, no. 2 (2004): 203–13. http://dx.doi.org/10.1119/1.1624111.

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Podlevskii, B. M. "Self-adjoint polynomial operator pencils, spectrally equivalent to self-adjoint operators." Ukrainian Mathematical Journal 36, no. 5 (1985): 498–500. http://dx.doi.org/10.1007/bf01086780.

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Antoniou, I., and S. A. Shkarin. "Decay spectrum and decay subspace of normal operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 6 (2001): 1245–55. http://dx.doi.org/10.1017/s0308210500001372.

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Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators Ap, Aac and Asc such that there exists an orthonormal basis of eigenvectors for the operator Ap, the operator Aac has purely absolutely continuous spectrum and the operator Asc has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component Asc into a direct sum of two self-adjoint operators and . The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.
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Berkics, Péter. "On Self-Adjoint Linear Relations." Mathematica Pannonica 27_NS1, no. 1 (2021): 1–7. http://dx.doi.org/10.1556/314.2020.00001.

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A linear operator on a Hilbert space , in the classical approach of von Neumann, must be symmetric to guarantee self-adjointness. However, it can be shown that the symmetry could be omitted by using a criterion for the graph of the operator and the adjoint of the graph. Namely, S is shown to be densely defined and closed if and only if .In a more general setup, we can consider relations instead of operators and we prove that in this situation a similar result holds. We give a necessary and sufficient condition for a linear relation to be densely defined and self-adjoint.
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Pavić, Zlatko. "Inequalities of Convex Functions and Self-Adjoint Operators." Journal of Operators 2014 (February 9, 2014): 1–5. http://dx.doi.org/10.1155/2014/382364.

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The paper offers generalizations of the Jensen-Mercer inequality for self-adjoint operators and generally convex functions. The obtained results are applied to define the quasi-arithmetic operator means without using operator convexity. The version of the harmonic-geometric-arithmetic operator mean inequality is derived as an example.
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Ghaedrahmati, Arezoo, and Ali Sameripour. "Investigation of the Spectral Properties of a Non-Self-Adjoint Elliptic Differential Operator." International Journal of Mathematics and Mathematical Sciences 2021 (May 13, 2021): 1–7. http://dx.doi.org/10.1155/2021/5564552.

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Non-self-adjoint operators have many applications, including quantum and heat equations. On the other hand, the study of these types of operators is more difficult than that of self-adjoint operators. In this paper, our aim is to study the resolvent and the spectral properties of a class of non-self-adjoint differential operators. So we consider a special non-self-adjoint elliptic differential operator (Au)(x) acting on Hilbert space and first investigate the spectral properties of space H 1 = L 2 Ω 1 . Then, as the application of this new result, the resolvent of the considered operator in ℓ -dimensional space Hilbert H ℓ = L 2 Ω ℓ is obtained utilizing some analytic techniques and diagonalizable way.
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Anastassiou, George A. "Self adjoint operator harmonic polynomials induced Chebyshev-Gruss inequalities." Studia Universitatis Babes-Bolyai Matematica 62, no. 1 (2017): 39–56. http://dx.doi.org/10.24193/subbmath.2017.0004.

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Kudryashov, Yu L. "Dilatations of Linear Operators." Contemporary Mathematics. Fundamental Directions 66, no. 2 (2020): 209–20. http://dx.doi.org/10.22363/2413-3639-2020-66-2-209-220.

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The article is devoted to building various dilatations of linear operators. The explicit construction of a unitary dilation of a compression operator is considered. Then the J -unitary dilatation of a bounded operator is constructed by means of the operator knot concept of a bounded linear operator. Using the Pavlov method, we construct the self-adjoint dilatation of a bounded dissipative operator. We consider spectral and translational representations of the self-adjoint dilatation of a densely defined dissipative operator with nonempty set of regular points. Using the concept of an operator knot for a bounded operator and the Cayley transform, we introduce an operator knot for a linear operator. By means of this concept, we construct the J -self-adjoint dilatation of a densely defined operator with a regular point. We obtain conditions of isomorphism of extraneous dilations and their minimality.
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Walker, Philip W. "An expansion theory for non-self-adjoint boundary-value problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 108, no. 1-2 (1988): 11–26. http://dx.doi.org/10.1017/s0308210500026470.

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SynopsisThis paper deals with two-point boundary-value problems for ordinary differential equations and the operators which they induce in the appropriate Hilbert space. The problems arenot required to be self-adjoint. No auxiliary condition such as Birkhoff-regularity is imposed. If T is such an operator, it may well have no meaningful spectral structure. It is shown, however, that when T is composed with its adjoint, the result is a non-negative self-adjoint differential operator. The eigenvalues and eigenfunctions of this composite operator are used to delineate the domain, action, range, and generalised inverse of T.
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Karabash, I. M., and S. Hassi. "Similarity between J-Self-Adjoint Sturm--Liouville Operators with Operator Potential and Self-Adjoint Operators." Mathematical Notes 78, no. 3-4 (2005): 581–85. http://dx.doi.org/10.1007/s11006-005-0159-z.

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Dissertations / Theses on the topic "Self-adjoint operator"

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Redparth, Paul Robert. "On the spectral and pseudospectral properties of non self adjoint Schrödinger operators". Thesis, King's College London (University of London), 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249528.

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Mortad, Mohammed Hichem. "Normal products of self-adjoint operators and self-adjointness of the perturbed wave operator on L²(Rn)." Thesis, University of Edinburgh, 2003. http://hdl.handle.net/1842/15434.

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This thesis contains five chapters. The first two are devoted to the background which consists of integration, Fourier analysis, distributions and linear operators in Hilbert spaces. The third chapter is a generalization of a work done by Albrecht-Spain in 2000. We give a shorter proof of the main theorem they proved for bounded operators and we generalize it to unbounded operators. We give a counterexample that shows that the result fails to be true for another class of operators. We also say why it does not hold. In chapters four and five, the idea is the same, that is to find classes of unbounded, real-valued V<i>s </i>for which  + <i>V</i> is self-adjoint on <i>D</i>(), where  is the wave operator. Throughout these two chapters we will see how different the Laplacian and the wave operator can be.
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Thelwall, Michael Arijan. "Bimodule theory in the study of non-self-adjoint operator algebras." Thesis, Lancaster University, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280735.

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Nguyen, Thi-Hien. "Etude de l'asymptotique du phénomène d'augmentation de diffusivité dans des flots à grande vitesse." Thesis, Brest, 2017. http://www.theses.fr/2017BRES0072/document.

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En application, on souhaite générer des nombres aléatoires avec une loi précise (méthode de Monte Carlo par chaines de Markov - MCMC (Markov Chaine Monte Carlo)). La méthode consiste à trouver une diffusion qui a la loi invariante souhaitée et à montrer la convergence de cette diffusion vers son équilibre avec une vitesse exponentielle. L’exposant de cette convergence est le trou spectral du générateur. Il a été montré par Chii-Ruey Hwang, Shu-Yin Hwang-Ma, et Shuenn-Jyi Sheu qu’on peut agrandir le trou spectral, en rajoutant un terme non-symétrique au générateur auto-adjoint (souvent utilisé en MCMC). Ceci correspond à passer d’une diffusion réversible (en detailed balance) à une diffusion non réversible. Un moyen de construire une diffusion non-réversible avec la même mesure invariante est de rajouter un flot incompressible à la dynamique de la diffusion réversible.Dans cette thèse, nous étudions le comportement de la diffusion lorsqu’on accélère le flot sous-jacent en multipliant le champ des vecteurs qui le décrit par une grande constante. P. Constantin, A.Kisekev, L.Ryzhik et A.Zlatoš (2008) ont montré que si le flot était faiblement mélangeant alors l’accélération du flot suffisait pour faire converger la diffusion vers son équilibre en un temps fini. Dans ce travail, on explicite la vitesse de ce phénomène sous une condition de corrélation du flot. L’article de B. Franke, C.-R.Hwang, H.-M. Pai et S.-J. Sheu (2010) donne l’expression asymptotique du trou spectral lorsque le flot sous-jacent est accéléré vers l’infini. Ici aussi, on s’intéresse à la vitesse avec laquelle le phénomène se manifeste. Dans un premier temps, nous étudions le cas particulier d’une diffusion du type Ornstein-Uhlenbeck qui est perturbée par un flot préservant la mesure gaussienne. Dans ce cas, grâce à un résultat de G. Metafune, D. Pallara et E. Priola (2002), nous pouvons réduire l’étude du spectre du générateur à des valeurs propres d’une famille de matrices. Nous étudions ce problème avec des méthodes de développement limité des valeurs propres. Ce problème est résolu explicitement dans cette thèse et nous donnons aussi une borne pour le rayon de convergence du développement. Nous généralisons ensuite cette méthode dans le cas d’une diffusion générale de façon formelle. Ces résultats peuvent être utiles pour avoir une première idée sur les vitesses de convergence du trou spectral décrites dans l’article de Franke et al. (2010)<br>In application, we would like to generate random numbers with a precise law MCMC (Markov Chaine Monte Carlo). The method consists in finding a diffusion which has the desired invariant law and in showing the convergence of this diffusion towards its equilibrium with an exponential rate. The exponent of this convergence is the spectral gap of the generator. It was shown by C.-R. Hwang, S.-Y. Hwang-Ma and S.-J. Sheu that the spectral gap can grow up by adding a non-symmetric term to the self-adjoint generator.This corresponds to passing from a reversible diffusion to a non-reversible diffusion. A means of constructing a non-reversible diffusion with the same invariant measure is to add an incompressible flow to the dynamics of the reversible diffusion.In this thesis, we study the behavior of diffusion when the flow is accelerated by multiplying the field of the vectors which describes it by a large constant. In 2008, P. Constantin, A. Kisekev, L. Ryzhik and A. Zlatoˇs have shown that if the flow was weakly mixing then the acceleration of the flow was sufficient to converge the diffusion towards its equilibrium after finite time. In this work, the speed of this phenomenon is explained under a condition of correlation of the flow. The article by B. Franke, C.-R.Hwang, H.-M. Pai and S.-J.Sheu (2010) gives the asymptotic expression of the spectral gap when the large constant goes to infinity. Here we are also interested in the speed with which the phenomenon manifests itself. First, we study the special case of an Ornstein-Uhlenbeck diffusion which is perturbed by a flow preserving the Gaussian measure. In this case, thanks to a result of G. Metafune, D. Pallara and E. Priola (2002), we can reduce the study of the generator spectrum to eigenvalues of a family of matrices. We study this problem with methods of limited development of eigenvalues. This problem is solved explicitly in this thesis and we also give a boundary for the convergence radius of the development. We then generalize this method in the case of a general diffusion in a formal way. These results may be useful to have a first idea on the speeds of convergence of the spectral gap described in the article by Franke et al. (2010)
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Michel, Patricia L. "Eigenvalue gaps for self-adjoint operators." Diss., Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/28795.

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Strömberg, Roland. "Spectral Theory for Bounded Self-adjoint Operators." Thesis, Uppsala University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121364.

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Verri, Alessandra Aparecida. "O átomo de hidrogênio em 1, 2 e 3 dimensões." Universidade Federal de São Carlos, 2007. https://repositorio.ufscar.br/handle/ufscar/5848.

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Made available in DSpace on 2016-06-02T20:28:22Z (GMT). No. of bitstreams: 1 1452.pdf: 916103 bytes, checksum: 40179df116306bc34414ecc8e0c08457 (MD5) Previous issue date: 2007-08-10<br>Financiadora de Estudos e Projetos<br>In this work we study the Hamiltonian of the hydrogen atom in 1, 2 and 3 dimensions. Especifically, it is defined as a self-adjoint operator in the Hilbert space L2(Rn), n = 1, 2, 3. Nevertheless, the main goal is to study the hydrogen atom 1-D. Particularly, for this is model we address some problens related to the singularity of the Coulomb potential.<br>Neste trabalho vamos estudar o Hamiltoniano do átomo de hidrogênio em 1, 2 e 3 dimensões. Especificamente, queremos defini-lo como um operador auto-adjunto no espaço de Hilbert L2(Rn), n = 1, 2, 3. No entanto, o principal objetivo é estudar o átomo de hidrogênio 1-D. Em particular, para este modelo, abordaremos algumas questões relacionadas à singularidade do potencial de Coulomb &#8722;1/|x|.
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Klein, Guillaume. "Stabilisation et asymptotique spectrale de l’équation des ondes amorties vectorielle." Thesis, Strasbourg, 2018. http://www.theses.fr/2018STRAD050/document.

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Dans cette thèse nous considérons l’équation des ondes amorties vectorielle sur une variété riemannienne compacte, lisse et sans bord. L’amortisseur est ici une fonction lisse allant de la variété dans l’espace des matrices hermitiennes de taille n. Les solutions de cette équation sont donc à valeurs vectorielles. Nous commençons dans un premier temps par calculer le meilleur taux de décroissance exponentiel de l’énergie en fonction du terme d’amortissement. Ceci nous permet d’obtenir une condition nécessaire et suffisante la stabilisation forte de l’équation des ondes amorties vectorielle. Nous mettons aussi en évidence l’apparition d’un phénomène de sur-amortissement haute fréquence qui n’existait pas dans le cas scalaire. Dans un second temps nous nous intéressons à la répartition asymptotique des fréquences propres de l’équation des ondes amorties vectorielle. Nous démontrons que, à un sous ensemble de densité nulle près, l’ensemble des fréquences propres est contenu dans une bande parallèle à l’axe imaginaire. La largeur de cette bande est déterminée par les exposants de Lyapunov d’un système dynamique défini à partir du coefficient d’amortissement<br>In this thesis we are considering the vectorial damped wave equation on a compact and smooth Riemannian manifold without boundary. The damping term is a smooth function from the manifold to the space of Hermitian matrices of size n. The solutions of this équation are thus vectorial. We start by computing the best exponential energy decay rate of the solutions in terms of the damping term. This allows us to deduce a sufficient and necessary condition for strong stabilization of the vectorial damped wave equation. We also show the appearance of a new phenomenon of high-frequency overdamping that did not exists in the scalar case. In the second half of the thesis we look at the asymptotic distribution of eigenfrequencies of the vectorial damped wave equation. Were show that, up to a null density subset, all the eigenfrequencies are in a strip parallel to the imaginary axis. The width of this strip is determined by the Lyapunov exponents of a dynamical system defined from the damping term
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Novak, Radek. "Mathematical analysis of Quantum mechanics with non-self-adjoint operators." Thesis, Nantes, 2018. http://www.theses.fr/2018NANT4062/document.

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L'importance des opérateurs non auto-adjoints dans la physique moderne augmente chaque jour, car ils commencent à jouer un rôle plus important dans la mécanique quantique. Cependant, la signification de leur examen est beaucoup plus récente que l'intérêt pour l'examen des opérateurs auto-adjoints. Ainsi, étant donné que de nombreuses techniques auto-adjointes ne sont pas généralisées à ce contexte, il n’existe pas beaucoup de méthodes bien développées pour examiner leurs propriétés. Cette thèse vise à contribuer à combler cette lacune et démontre plusieurs modèles non auto-adjoints et les moyens de leur étude. Les sujets comprennent le pseudo-spectre comme un analogue approprié du spectre, un modèle d'une guide d'onde avec un gain et une perte équilibrés à la frontière et l'équation de Kramers-Fokker-Planck avec un potentiel à courte distance<br>The importance of non-self-adjoint operators in modern physics increases every day as they start to play more prominent role in Quantum mechanics. However, the significance of their examination is much more recent than the interest in the examination of their selfadjoint counterparts. Thus, since many selfadjoint techniques fail to be generalized to this context, there are not many well-developed methods for examining their properties. This thesis aims to contribute to filling this gap and demonstrates several non-self-adjoint models and the means of their study. The topics include pseudospectrum as a suitable analogue of the spectrum, a model of a quantum layer with balanced gain and loss at the boundary, and the Kramers-Fokker-Planck equation with a short-range potential
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Hobiny, Aatef. "Enclosures for the eigenvalues of self-adjoint operators and applications to Schrodinger operators." Thesis, Heriot-Watt University, 2014. http://hdl.handle.net/10399/2790.

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This thesis concerns how to compute upper and lower bounds for the eigenvalues of self-adjoint operators. We discuss two different methods: the so-called quadratic method and the Zimmermann-Mertins method. We know that the classical methods of computing the spectrum of a self-adjoint operator often lead to spurious eigenvalues in gaps between two parts of the essential spectrum. The methods to be examined have been studied recently in connection with the phenomenon of spectral pollution. In the first part of the thesis we show how to obtain enclosures of the eigenvalues in both the quadratic method and the Zimmermann-Mertins method. We examine the convergence properties of these methods for computing corresponding upper and lower bounds in the case of semi-definite self-adjoint operators with compact resolvent. In the second part of the thesis we find concrete asymptotic bounds for the size of the enclosure and study their optimality in the context of one-dimensional Schr¨odinger operators. The effectiveness of these methods is then illustrated by numerical experiments on the harmonic and the anharmonic oscillators. We compare these two methods, and establish which one is better suited in terms of accuracy and efficiency.
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Books on the topic "Self-adjoint operator"

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Veliev, Oktay. Non-self-adjoint Schrödinger Operator with a Periodic Potential. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72683-6.

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Schmüdgen, Konrad. Unbounded Self-adjoint Operators on Hilbert Space. Springer Netherlands, 2012.

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Kopachevsky, Nikolay D. Operator Approach to Linear Problems of Hydrodynamics: Volume 1: Self-adjoint Problems for an Ideal Fluid. Birkhäuser Basel, 2001.

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V, Tyutin I., Voronov B. L, and SpringerLink (Online service), eds. Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials. Birkhäuser Boston, 2012.

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Dunford, Nelson. Linear operators.: Self adjoint operators in Hilbert space. Interscience Publishers, 1988.

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Ilʹin, V. A. Spectral theory of differential operators: Self-adjoint differential operators. Consultants Bureau, 1995.

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Möller, Manfred, Dr. rer. nat. habil., ed. Non-self-adjoint boundary eigenvalue problems. Elsevier, 2003.

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Schmüdgen, Konrad. Unbounded Self-adjoint Operators on Hilbert Space. Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-4753-1.

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Spectral theory of families of self-adjoint operators. Kluwer Academic Publishers, 1991.

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Samoilenko, Y. S. Spectral Theory of Families of Self-Adjoint Operators. Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3806-2.

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Book chapters on the topic "Self-adjoint operator"

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Stulpe, Werner. "Self-Adjoint Operator." In Compendium of Quantum Physics. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-70626-7_196.

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Rodman, Leiba. "Self-Adjoint Operator Polynomials." In An Introduction to Operator Polynomials. Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-9152-3_6.

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Power, S. C. "Partly Self-Adjoint Limit Algebras." In Operator Algebras and Applications. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5500-7_13.

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Anastassiou, George A. "Self Adjoint Operator Ostrowski Inequalities." In Intelligent Comparisons II: Operator Inequalities and Approximations. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51475-8_5.

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Gohberg, Israel, and Seymour Goldberg. "Spectral Theory of Compact Self Adjoint Operators." In Basic Operator Theory. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-5985-5_3.

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Gitman, D. M., I. V. Tyutin, and B. L. Voronov. "Dirac Operator with Coulomb Field." In Self-adjoint Extensions in Quantum Mechanics. Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-4662-2_9.

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Maher, Philip J. "Self-Adjoint and Positive Approximants." In Operator Approximant Problems Arising from Quantum Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61170-9_3.

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Anastassiou, George A. "Self Adjoint Operator Chebyshev-Grüss Inequalities." In Intelligent Comparisons II: Operator Inequalities and Approximations. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51475-8_7.

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Schmüdgen, Konrad. "Self-Adjoint Representations of Commutative *-Algebras." In Unbounded Operator Algebras and Representation Theory. Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-7469-4_9.

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Tkachenko, Vadim. "Non-self-adjoint Periodic Dirac Operators." In Operator Theory, System Theory and Related Topics. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8247-7_22.

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Conference papers on the topic "Self-adjoint operator"

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Bairamov, Elgiz, Meltem Sertbaş, and Zameddin I. Ismailov. "Self-adjoint extensions of singular third-order differential operator and applications." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4893826.

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Zakirova, G. A. "An approximate solution of inverse spectral problem for perturbed self-adjoint operator." In 2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM). IEEE, 2016. http://dx.doi.org/10.1109/icieam.2016.7911714.

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Kadchenko, S. I., A. I. Kadchenko, G. A. Zakirova, and S. I. Kadchenko. "The numerical method of solving of inverse spectral problems generated by perturbed self-adjoint operator." In 2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM). IEEE, 2016. http://dx.doi.org/10.1109/icieam.2016.7911720.

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Ashyralyev, Allaberen, Ozgur Yildirim, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Second Order of Accuracy Stable Difference Schemes for Hyperbolic Problems Subject to Nonlocal Conditions with Self-Adjoint Operator." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636801.

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Opmeer, M. R., and O. V. Iftime. "A representation of all bounded self-adjoint solutions of the algebraic Riccati equation for systems with an unbounded observation operator." In 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601). IEEE, 2004. http://dx.doi.org/10.1109/cdc.2004.1428899.

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Balas, Mark J. "Augmentation of Fixed Gain Controlled Infinite Dimensional Systems With Direct Adaptive Control." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-23179.

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Abstract Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. We augment this controller with a direct adaptive controller that will maintain stability of the full closed loop system even when the fixed gain controller fails to do so. We prove that the transmission zeros of the combined system are the original open loop transmission zeros, and the point spectrum of the controller alone. Therefore, the combined plant plus controller is Almost Strictly Dissipative (ASD) if and only if the original open loop system is minimum phase, and the fixed gain controller alone is exponentially stable. This result is true whether the fixed gain controller is finite or infinite dimensional. In particular this guarantees that a controller for an infinite dimensional plant based on a reduced -order approximation can be stabilized by augmentation with direct adaptive control to mitigate risks. These results are illustrated by application to direct adaptive control of general linear diffusion systems on a Hilbert space that are described by self-adjoint operators with compact resolvent.
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Manafov, Manaf Dzh. "Self-adjoint extensions of differential operators with potentials-point interactions." In 6TH INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS (IECMSA-2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5020478.

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8

Moarref, Rashad, Makan Fardad, and Mihailo R. Jovanovic. "Perturbation analysis of eigenvalues of a class of self-adjoint operators." In 2008 American Control Conference (ACC '08). IEEE, 2008. http://dx.doi.org/10.1109/acc.2008.4586615.

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9

SCHULTZE, BERND. "PROBLEMS CONCERNING THE DEFICIENCY INDICES OF SINGULAR SELF-ADJOINT ORDINARY DIFFERENTIAL OPERATORS." In Third Asian Mathematical Conference 2000. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777461_0045.

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"Spectral Analysis for One Class Non-Self-Adjoint Operators with Almost Periodic Potentials." In IBRAS 2021 INTERNATIONAL CONFERENCE ON BIOLOGICAL RESEARCH AND APPLIED SCIENCE. Juw, 2021. http://dx.doi.org/10.37962/ibras/2021/153.

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Reports on the topic "Self-adjoint operator"

1

Roberts, R. M. Spatial and angular variation and discretization of the self-adjoint transport operator. Office of Scientific and Technical Information (OSTI), 1996. http://dx.doi.org/10.2172/442191.

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2

Tygert, Mark. Fast Algorithms for the Solution of Eigenfunction Problems for One-Dimensional Self-Adjoint Linear Differential Operators. Defense Technical Information Center, 2005. http://dx.doi.org/10.21236/ada458901.

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