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|a 9783030367145
|q (electronic bk.)
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|z 9783030367138
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|a (MiAaPQ)EBC6111529
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|a (Au-PeEL)EBL6111529
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|a (OCoLC)1138959235
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|a MiAaPQ
|b eng
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|c MiAaPQ
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|a QA329-329.9
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|a Behrndt, Jussi.
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|a Boundary Value Problems, Weyl Functions, and Differential Operators.
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|a 1st ed.
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| 264 |
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|a Cham :
|b Springer International Publishing AG,
|c 2020.
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|c ©2020.
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| 300 |
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|a 1 online resource (775 pages)
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| 336 |
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|a text
|b txt
|2 rdacontent
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| 337 |
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|a computer
|b c
|2 rdamedia
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| 338 |
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|a online resource
|b cr
|2 rdacarrier
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| 490 |
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|a Monographs in Mathematics Series ;
|v v.108
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|a Intro -- Contents -- Preface -- 1 Introduction -- 2 Linear Relations in Hilbert Spaces -- 1.1 Elementary facts about linear relations -- 1.2 Spectra, resolvent sets, and points of regular type -- 1.3 Adjoint relations -- 1.4 Symmetric relations -- 1.5 Self-adjoint relations -- 1.6 Maximal dissipative and accumulative relations -- 1.7 Intermediate extensions and von Neumann's formulas -- 1.8 Adjoint relations and indefinite inner products -- 1.9 Convergence of sequences of relations -- 1.10 Parametric representations for relations -- 1.11 Resolvent operators with respect to a bounded operator -- 1.12 Nevanlinna families and their representations -- 3 Boundary Triplets and Weyl Functions -- 2.1 Boundary triplets -- 2.2 Boundary value problems -- 2.3 Associated γ-fields and Weyl functions -- 2.4 Existence and construction of boundary triplets -- 2.5 Transformations of boundary triplets -- 2.6 Kreın's formula for intermediate extensions -- 2.7 Kreın's formula for exit space extensions -- 2.8 Perturbation problems -- 4 Spectra, Simple Operators, and Weyl Functions -- 3.1 Analytic descriptions of minimal supports of Borel measures -- 3.2 Growth points of finite Borel measures -- 3.3 Spectra of self-adjoint relations -- 3.4 Simple symmetric operators -- 3.5 Eigenvalues and eigenspaces -- 3.6 Spectra and local minimality -- 3.7 Limit properties of Weyl functions -- 3.8 Spectra and local minimality for self-adjoint extensions -- 5 Operator Models for Nevanlinna Functions -- 4.1 Reproducing kernel Hilbert spaces -- 4.2 Realization of uniformly strict Nevanlinna functions -- 4.3 Realization of scalar Nevanlinna functions via L2-space models -- 4.4 Realization of Nevanlinna pairs and generalized resolvents -- 4.5 Kreın's formula for exit space extensions -- 4.6 Orthogonal coupling of boundary triplets.
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|a 6 Boundary Triplets and Boundary Pairs for Semibounded Relations -- 5.1 Closed semibounded forms and their representations -- 5.2 Ordering and monotonicity -- 5.3 Friedrichs extensions of semibounded relations -- 5.4 Semibounded self-adjoint extensions and their lower bounds -- 5.5 Boundary triplets for semibounded relations -- 5.6 Boundary pairs and boundary triplets -- 7 Sturm-Liouville Operators -- 6.1 Sturm-Liouville differential expressions -- 6.2 Maximal and minimal Sturm-Liouville differential operators -- 6.3 Regular and limit-circle endpoints -- 6.4 The case of one limit-point endpoint -- 6.5 The case of two limit-point endpoints and interface conditions -- 6.6 Exit space extensions -- 6.7 Weyl functions and subordinate solutions -- 6.8 Semibounded Sturm-Liouville expressions in the regular case -- 6.9 Closed semibounded forms for Sturm-Liouville equations -- 6.10 Principal and nonprincipal solutions of Sturm-Liouville equations -- 6.11 Semibounded Sturm-Liouville operators and the limit-circle case -- 6.12 Semibounded Sturm-Liouville operators and the limit-point case -- 6.13 Integrable potentials -- 8 Canonical Systems of Differential Equations -- 7.1 Classes of integrable functions -- 7.2 Canonical systems of differential equations -- 7.3 Regular and quasiregular endpoints -- 7.4 Square-integrability of solutions of real canonical systems -- 7.5 Definite canonical systems -- 7.6 Maximal and minimal relations for canonical systems -- 7.7 Boundary triplets for the limit-circle case -- 7.8 Boundary triplets for the limit-point case -- 7.9 Weyl functions and subordinate solutions -- 7.10 Special classes of canonical systems -- 9 Schrödinger Operators on Bounded Domains -- 8.1 Rigged Hilbert spaces -- 8.2 Sobolev spaces, C2-domains, and trace operators -- 8.3 Trace maps for the maximal Schrödinger operator.
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|a 8.4 A boundary triplet for the maximal Schrödinger operator -- 8.5 Semibounded Schrödinger operators -- 8.6 Coupling of Schrödinger operators -- 8.7 Bounded Lipschitz domains -- Integral Representations of Nevanlinna Functions -- A.1 Borel transforms and their Stieltjes inversion -- A.2 Scalar Nevanlinna functions -- A.3 Operator-valued integrals -- A.4 Operator-valued Nevanlinna functions -- A.5 Kac functions -- A.6 Stieltjes and inverse Stieltjes functions -- Self-adjoint Operators and Fourier Transforms -- B.1 The scalar case -- B.2 The vector case -- Sums of Closed Subspaces in Hilbert Spaces -- Factorization of Bounded Linear Operators -- Notes -- Bibliography -- List of Symbols -- Index.
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|a Description based on publisher supplied metadata and other sources.
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| 590 |
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|a Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2023. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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| 655 |
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|a Electronic books.
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| 700 |
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|a Hassi, Seppo.
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| 700 |
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|a de Snoo, Henk.
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| 776 |
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|i Print version:
|a Behrndt, Jussi
|t Boundary Value Problems, Weyl Functions, and Differential Operators
|d Cham : Springer International Publishing AG,c2020
|z 9783030367138
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| 797 |
2 |
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|a ProQuest (Firm)
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| 830 |
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0 |
|a Monographs in Mathematics Series
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| 856 |
4 |
0 |
|u https://ebookcentral.proquest.com/lib/matrademy/detail.action?docID=6111529
|z Click to View
|
