Boundary value problems, Weyl functions, and differential operators /
"A comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions."--Back cover.
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| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham, Switzerland :
Birkhäuser, Springer,
[2020]
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| Series: | Monographs in mathematics ;
v. 108. |
| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- Preface
- Introduction
- Linear Relations in Hilbert Spaces
- Elementary facts about linear relations
- Spectra, resolvent sets, and points of regular type
- Adjoint relations
- Symmetric relations
- Self-adjoint relations
- Maximal dissipative and accumulative relations
- Intermediate extensions and von Neumann's formulas
- Adjoint relations and indefinite inner products
- Convergence of sequences of relations
- Parametric representations for relations
- Resolvent operators with respect to a bounded operator
- Nevanlinna families and their representations
- Boundary Triplets and Weyl Functions
- Boundary triplets
- Boundary value problems
- Associated ...-fields and Weyl functions
- Existence and construction of boundary triplets
- Transformations of boundary triplets
- Kreĭn's formula for intermediate extensions
- Kreĭn's formula for exit space extensions
- Perturbation problems
- Spectra, Simple Operators, and Weyl Functions
- Analytic descriptions of minimal supports of Borel measures
- Growth points of finite Borel measures
- Spectra of self-adjoint relations
- Simple symmetric operators
- Eigenvalues and eigenspaces
- Spectra and local minimality
- Limit properties of Weyl functions
- Spectra and local minimality for self-adjoint extensions
- Operator Models for Nevanlinna Functions
- Reproducing kernel Hilbert spaces
- Realization of uniformly strict Nevanlinna functions
- Realization of scalar Nevanlinna functions via L²-space models
- Realization of Nevanlinna pairs and generalized resolvents
- Kreĭn's formula for exit space extensions
- Orthogonal coupling of boundary triplets
- Boundary Triplets and Boundary Pairs for Semibounded Relations
- Closed semibounded forms and their representations
- Ordering and monotonicity
- Friedrichs extensions of semibounded relations
- Semibounded self-adjoint extensions and their lower bounds
- Boundary triplets for semibounded relations
- Boundary pairs and boundary triplets
- Sturm-Liouville Operators
- Sturm-Liouville differential expressions
- Maximal and minimal Sturm-Liouville differential operators
- Regular and limit-circle endpoints
- The case of one limit-point endpoint
- The case of two limit-point endpoints and interface conditions
- Exit space extensions
- Weyl functions and subordinate solutions
- Semibounded Sturm-Liouville expressions in the regular case
- Closed semibounded forms for Sturm-Liouville equations
- Principal and nonprincipal solutions of Sturm-Liouville equations
- Semibounded Sturm-Liouville operators and the limit-circle case
- Semibounded Sturm-Liouville operators and the limit-point case
- Integrable potentials
- Canonical Systems of Differential Equations
- Classes of integrable functions
- Canonical systems of differential equations
- Regular and quasiregular endpoints
- Square-integrability of solutions of real canonical systems
- Definite canonical systems
- Maximal and minimal relations for canonical systems
- Boundary triplets for the limit-circle case
- Boundary triplets for the limit-point case
- Weyl functions and subordinate solutions
- Special classes of canonical systems
- Schrodinger Operators on Bounded Domains
- Rigged Hilbert spaces
- Sobolev spaces, C²-domains, and trace operators
- Trace maps for the maximal Schrödinger operator
- A boundary triplet for the maximal Schrödinger operator
- Semibounded Schrödinger operators
- Coupling of Schrödinger operators
- Bounded Lipschitz domains
- Integral Representations of Nevanlinna Functions
- Borel transforms and their Stieltjes inversion
- Scalar Nevanlinna functions
- Operator-valued integrals
- Operator-valued Nevanlinna functions
- Kac functions
- Stieltjes and inverse Stieltjes functions
- Self-adjoint Operators and Fourier Transforms
- The scalar case
- The vector case
- Sums of Closed Subspaces in Hilbert Spaces
- Factorization of Bounded Linear Operators
- Notes
- Bibliography
- List of Symbols
- Index.
