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Author:
Behrndt, Jussi, author.
Title:
Boundary value problems, Weyl functions, and differential operators / Jussi Behrndt, Seppo Hassi, Henk de Snoo.
Publisher:
BirkhäuserSpringer,
Copyright Date:
2020
Description:
vii, 772 pages : illustrations ; 25 cm.
Subject:
Boundary value problems.
Boundary value problems--Weyl theory.
Differential operators.
Spectral theory (Mathematics)
Boundary value problems.
Boundary value problems--Weyl theory.
Differential operators.
Spectral theory (Mathematics)
Other Authors:
Hassi, Seppo, author.
Snoo, Henk de, author.
Notes:
Includes bibliographical references (pages 721-764) and index.
Contents:
Index. Introduction -- Factorization of Bounded Linear Operators -- 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.
Summary:
"A comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions."--Back cover.
Series:
Monographs in mathematics, 1017-0480 ; Volume 108
ISBN:
3030367134
9783030367138
OCLC:
(OCoLC)1140081422
Locations:
OVUX522 -- University of Iowa Libraries (Iowa City)

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