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Books on the topic 'Self-adjoint operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

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

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2

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

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3

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

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4

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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5

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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6

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

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7

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

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8

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

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9

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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10

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

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11

Bernstein, Herbert J. An inequality for self-adjoint operators on a Hilbert space. New York: Courant Institute of Mathematical Sciences, New York University, 1985.

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12

Bernstein, Herbert J. An inequality for self-adjoint operators on a Hilbert space. New York: Courant Institute of Mathematical Sciences, New York University, 1985.

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13

Sjöstrand, Johannes. Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10819-9.

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14

Tembo, Isaac D. Self-adjoint differential operators and norm estimates of integral operators on a finite interval. Birmingham: University of Birmingham, 1996.

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15

Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates. Providence, R.I: American Mathematical Society, 2011.

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16

Koshmanenko, Volodymyr, and Mykola Dudkin. The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29535-0.

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17

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

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18

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

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19

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

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20

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. Boston: Birkhäuser Boston, 2012.

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21

Agranovich, V. M. Non-Self Adjoint Elliptic Operators. Springer-Verlag, 1995.

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22

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

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23

Samoilenko, A. M. Spectral Theory of Families of Self-Adjoint Operators. Springer, 1991.

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24

Dunford, Neilson, and Jacob T. Schwartz. Linear Operators, Spectral Theory, Self Adjoint Operators in Hilbert Space, Part 2. Wiley-Interscience, 1988.

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25

Sjöstrand, Johannes. Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations. Birkhäuser, 2019.

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26

Gitman, Dmitry, Igor Tyutin, and Boris Voronov. Self-adjoint Extensions As a Quantization Problem (Progress in Mathematical Physics). Springer, 2007.

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27

Mennicken, R., and M. Möller. Non-Self-Adjoint Boundary Eigenvalue Problems (North-Holland Mathematics Studies). North Holland, 2003.

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28

Koshmanenko, Volodymyr, Mykola Dudkin, and Nataliia Koshmanenko. The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators. Birkhäuser, 2016.

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29

Koshmanenko, Volodymyr, Mykola Dudkin, and Nataliia Koshmanenko. The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators. Birkhäuser, 2018.

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30

Edmunds, D. E., and W. D. Evans. Unbounded Linear Operators. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0003.

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This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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31

Edmunds, D. E., and W. D. Evans. Essential Spectra. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0009.

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In this chapter, various essential spectra are studied. For a closed operator in a Banach space, a number of different sets have been used for the essential spectrum, the sets being identical for a self-adjoint operator in a Hilbert space. As well as the essential spectra, the changes that occur when the operator is perturbed are discussed. Constant-coefficient differential operators are studied in detail.

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32

Edmunds, D. E., and W. D. Evans. Second-Order Differential Operators on Arbitrary Open Sets. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0007.

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In this chapter, three different methods are described for obtaining nice operators generated in some L2 space by second-order differential expressions and either Dirichlet or Neumann boundary conditions. The first is based on sesquilinear forms and the determination of m-sectorial operators by Kato’s First Representation Theorem; the second produces an m-accretive realization by a technique due to Kato using his distributional inequality; the third has its roots in the work of Levinson and Titchmarsh and gives operators T that are such that iT is m-accretive. The class of such operators includes the self-adjoint operators, even ones that are not bounded below. The essential self-adjointness of Schrödinger operators whose potentials have strong local singularities are considered, and the quantum-mechanical interpretation of essential self-adjointness is discussed.

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33

Forrester, Peter. Wigner matrices. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.21.

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This article reviews some of the important results in the study of the eigenvalues and the eigenvectors of Wigner random matrices, that is. random Hermitian (or real symmetric) matrices with iid entries. It first provides an overview of the Wigner matrices, introduced in the 1950s by Wigner as a very simple model of random matrices to approximate generic self-adjoint operators. It then considers the global properties of the spectrum of Wigner matrices, focusing on convergence to the semicircle law, fluctuations around the semicircle law, deviations and concentration properties, and the delocalization of the eigenvectors. It also describes local properties in the bulk and at the edge before concluding with a brief analysis of the known universality results showing how much the behaviour of the spectrum is insensitive to the distribution of the entries.

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34

Edmunds, D. E., and W. D. Evans. Estimates for the Singular Values of −Δ‎ + q when q is Complex. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0012.

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This chapter considers the Schrödinger operator −Δ‎ + q with q complex. In this case the operator is not self-adjoint and so the analysis of Chapter XI does not apply. It is the distribution of the singular values that is now considered, the technique used being again the localization to cubes forming a covering of Ω‎, together with the Max–Min Principle. Some results are obtained concerning the sequence class lp to which the singular numbers and eigenvalues belong.

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35

Kopachevskii, Nikolay D., and Selim G. Krein. Operator Approach in Linear Problems of Hydrodynamics: Volume 1: Self-adjoint Problems for an Ideal Fluid (Operator Theory: Advances and Applications). Birkhauser, 2001.

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