Relevant bibliographies by topics / Self-adjoint operators

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  2. Dissertations / Theses
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Academic literature on the topic 'Self-adjoint operators'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Self-adjoint operators"

1

Araujo, Vanilse S., F. A. B. Coutinho, and J. Fernando Perez. "Operator domains and self-adjoint operators." American Journal of Physics 72, no. 2 (February 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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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 (September 2005): 581–85. http://dx.doi.org/10.1007/s11006-005-0159-z.

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Hiptmair, Ralf, Peter Robert Kotiuga, and Sébastien Tordeux. "Self-adjoint curl operators." Annali di Matematica Pura ed Applicata 191, no. 3 (February 25, 2011): 431–57. http://dx.doi.org/10.1007/s10231-011-0189-y.

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Molnár, Lajos, and Peter Šemrl. "Elementary operators on self-adjoint operators." Journal of Mathematical Analysis and Applications 327, no. 1 (March 2007): 302–9. http://dx.doi.org/10.1016/j.jmaa.2006.04.039.

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DAVIES, E. B. "NON-SELF-ADJOINT DIFFERENTIAL OPERATORS." Bulletin of the London Mathematical Society 34, no. 05 (September 2002): 513–32. http://dx.doi.org/10.1112/s0024609302001248.

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Toland, J. F. "Self-Adjoint Operators and Cones." Journal of the London Mathematical Society 53, no. 1 (February 1996): 167–83. http://dx.doi.org/10.1112/jlms/53.1.167.

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Miyao, Tadahiro. "Strongly Supercommuting Self-Adjoint Operators." Integral Equations and Operator Theory 50, no. 4 (December 2004): 505–35. http://dx.doi.org/10.1007/s00020-003-1233-0.

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Sebestyén, Zoltán, and Zsigmond Tarcsay. "Characterizations of essentially self-adjoint and skew-adjoint operators." Studia Scientiarum Mathematicarum Hungarica 52, no. 3 (September 2015): 371–85. http://dx.doi.org/10.1556/012.2015.52.3.1300.

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An extension of von Neumann’s characterization of essentially selfadjoint operators is given among not necessarily densely defined symmetric operators which are assumed to be closable. Our arguments are of algebraic nature and follow the idea of [1].
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Gomilko, A. M. "On the theory ofJ-self-adjoint perturbations of self-adjoint operators." Functional Analysis and Its Applications 30, no. 1 (January 1996): 47–49. http://dx.doi.org/10.1007/bf02509558.

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

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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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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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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
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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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 Vs for which  + V is self-adjoint on D(), 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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Shlapunov, Alexander. "Iterations of self-adjoint operators and their applications to elliptic systems." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2540/.

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Let Hsub(0), Hsub(1) be Hilbert spaces and L : Hsub(0) -> Hsub(1) be a linear bounded operator with ||L|| ≤ 1. Then L*L is a bounded linear self-adjoint non-negative operator in the Hilbert space Hsub(0) and one can use the Neumann series ∑∞sub(v=0)(I - L*L)v L*f in order to study solvability of the operator equation Lu = f. In particular, applying this method to the ill-posed Cauchy problem for solutions to an elliptic system Pu = 0 of linear PDE's of order p with smooth coefficients we obtain solvability conditions and representation formulae for solutions of the problem in Hardy spaces whenever these solutions exist. For the Cauchy-Riemann system in C the summands of the Neumann series are iterations of the Cauchy type integral. We also obtain similar results 1) for the equation Pu = f in Sobolev spaces, 2) for the Dirichlet problem and 3) for the Neumann problem related to operator P*P if P is a homogeneous first order operator and its coefficients are constant. In these cases the representations involve sums of series whose terms are iterations of integro-differential operators, while the solvability conditions consist of convergence of the series together with trivial necessary conditions.
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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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Bruder, Andrea S. Littlejohn Lance L. "Applied left-definite theory the Jacobi polynomials, their Sobolev orthogonality, and self-adjoint operators /." Waco, Tex. : Baylor University, 2009. http://hdl.handle.net/2104/5327.

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Thesis (Ph.D.)--Baylor University, 2009.
Subscript in abstract: n and n=0 in {Pn([alpha],[beta])(x)} [infinity] n=0, [mu] in (f,g)[mu], and R in [integral]Rfgd[mu]. Superscript in abstract: ([alpha],[beta]) and [infinity] in {Pn([alpha],[beta])(x)} [infinity] n=0. Includes bibliographical references (p. 115-119).
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Chonchaiya, Ratchanikorn. "Computing the Spectra aand Pseudospectra of Non-Self Adjoint Random Operators Arising in Mathematical Physics." Thesis, University of Reading, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.533744.

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Lee, Gyou-Bong. "A study of the computation and convergence behavior of eigenvalue bounds for self-adjoint operators." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/39916.

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The convergence rates for the method of Weinstein and a variant method of Aronszajn known as "truncation including the remainder" are derived in terms of the containment gaps between exact and approximating subspaces, using analytical techniques that arise in part in the convergence analysis of finite element methods for differential eigenvalue problems. An example of a one dimensional Schrodinger operator with a potential is presented which arises in quantum mechanics. Examples using the recent eigenvector-free (EVF) method of Beattie and Goerisch are considered. Since the EVF method uses finite element trial functions as approximating vectors, it produces sparse and well-structured coefficient matrices. For these large-order sparse matrix eigenvalue problems, we adapt a spectral transformation Lanczos algorithm for finding a few wanted eigenvalues. For a few particular examples of vibration in beams and plates, convergence behavior is experimentally evaluated.
Ph. D.
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Books on the topic "Self-adjoint operators"

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

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

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

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

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

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

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

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Birman, M. Sh. Spectral theory of self-adjoint operators in Hilbert space. Dordrecht: D. Reidel Pub. Co., 1987.

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Birman, M. S., and M. Z. Solomjak. Spectral Theory of Self-Adjoint Operators in Hilbert Space. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-4586-9.

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Spectral theory of non-self-adjoint two-point differential operators. Providence, R.I: American Mathematical Society, 2000.

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Book chapters on the topic "Self-adjoint operators"

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Hislop, P. D., and I. M. Sigal. "Self-Adjoint Operators." In Introduction to Spectral Theory, 49–57. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-0741-2_5.

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Alt, Hans Wilhelm. "Self-adjoint operators." In Universitext, 389–418. London: Springer London, 2016. http://dx.doi.org/10.1007/978-1-4471-7280-2_12.

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Wong, M. W. "Self-Adjoint Operators." In Discrete Fourier Analysis, 113–16. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0116-4_16.

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Eidelman, Yuli, Vitali Milman, and Antonis Tsolomitis. "Self-adjoint operators." In Graduate Studies in Mathematics, 87–104. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/gsm/066/06.

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Blanchard, Philippe, and Erwin Brüning. "Self-adjoint Hamilton Operators." In Mathematical Methods in Physics, 313–16. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0049-9_23.

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Samoilenko, Y. S. "Anticommuting Self-Adjoint Operators." In Spectral Theory of Families of Self-Adjoint Operators, 152–64. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3806-2_10.

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Hall, Brian C. "Unbounded Self-Adjoint Operators." In Graduate Texts in Mathematics, 169–200. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7116-5_9.

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Surana, Karan S., and J. N. Reddy. "Self-Adjoint Differential Operators." In The Finite Element Method for Boundary Value Problems, 223–362. Boca Raton : CRC Press, 2017.: CRC Press, 2016. http://dx.doi.org/10.1201/9781315365718-5.

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Gitman, D. M., I. V. Tyutin, and B. L. Voronov. "Differential Operators." In Self-adjoint Extensions in Quantum Mechanics, 103–76. Boston: Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-4662-2_4.

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Moroşanu, Gheorghe. "Adjoint, Symmetric, and Self-adjoint Linear Operators." In Functional Analysis for the Applied Sciences, 201–16. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-27153-4_7.

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Conference papers on the topic "Self-adjoint operators"

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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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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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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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Došlý, Ondřej. "Oscillation and spectral properties of self-adjoint even order differential operators with middle terms." In The 7'th Colloquium on the Qualitative Theory of Differential Equations. Szeged: Bolyai Institute, SZTE, 2003. http://dx.doi.org/10.14232/ejqtde.2003.6.7.

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Wu, Xuqiang, and Bingen Yang. "Closed-Form Transient Response of One-Dimensional Continua." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-3843.

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Abstract Exact and closed-form transient response of general one-dimensional distributed dynamic systems subject to arbitrary external, initial and boundary disturbances is determined. Non-self-adjoint operators characterizing damping, gyroscopic and circulatory effects, and eigenvalue-dependent boundary conditions are considered. Through introduction of augmented operators, a closed-form modal expansion of the displacement and internal forces of the distributed system is derived. The eigenfunction expansion is realized in a spatial state-space formulation, which systematically yields exact eigensolutions, eigenfunction normalization coefficients, and modal coordinates. The proposed method is illustrated on a cantilever beam with end mass, damper and spring.
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Ibort, A. "Three lectures on global boundary conditions and the theory of self-adjoint extensions of the covariant Laplace-Beltrami and Dirac operators on Riemannian manifolds with boundary." In XX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS. AIP, 2012. http://dx.doi.org/10.1063/1.4733360.

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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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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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Reports on the topic "Self-adjoint operators"

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

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

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