Generalized boundary triples, II. Some applications of generalized boundary triples and form domain invariant Nevanlinna functions

DOI10.1002/mana.202000049MaRDI QIDQ6093924

Mark M. Malamud, Hassi, Seppo, Vladimir A. Derkach

Publication date: 9 October 2023

Published in: Mathematische Nachrichten (Search for Journal in Brave)

zbMATH Keywords

resolventboundary value problemWeyl functionsymmetric operatortrace operatorboundary tripleselfadjoint extensionGreen's identitiesDirichlet-to-Neumann type map

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of ordinary differential operators (47E05) General theory of partial differential operators (47F05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Dilations, extensions, compressions of linear operators (47A20) Parameter dependent boundary value problems for ordinary differential equations (34B08) Boundary value problems on infinite intervals for ordinary differential equations (34B40) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items

On the similarity of boundary triples of symmetric operators in Krein spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sturm-Liouville boundary value problems with operator potentials and unitary equivalence
• Elliptic differential operators on Lipschitz domains and abstract boundary value problems
• A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains
• The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates
• The Dirichlet-to-Neumann operator on rough domains
• Weyl function and spectral properties of self-adjoint extensions
• Boundary value problems for elliptic partial differential operators on bounded domains
• Spectral theory of elliptic operators in exterior domains
• 1-D Schrödinger operators with local point interactions on a discrete set
• Boundary relations and generalized resolvents of symmetric operators
• New analytically solvable models of relativistic point interactions
• The Dirichlet problem in non-smooth domains
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• Certain classes of extensions of a lacunary Hermitian operator
• The Laplacian with Robin boundary conditions on arbitrary domains
• Spectral enclosures for non-self-adjoint extensions of symmetric operators
• The inhomogeneous Dirichlet problem in Lipschitz domains
• The extension theory of Hermitian operators and the moment problem
• On the spectral theory of Gesztesy-Šeba realizations of 1-D Dirac operators with point interactions on a discrete set
• Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems
• Perturbation determinants for singular perturbations
• Scattering matrices and Dirichlet-to-Neumann maps
• Unitary equivalence of proper extensions of a symmetric operator and the Weyl function
• Sectorial forms and degenerate differential operators
• Boundary relations and their Weyl families
• Distributions and Operators
• M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems
• Maximal sectorial extensions and closed forms associated with them
• Robin boundary value problems on arbitrary domains
• On Kreĭn's extension theory of nonnegative operators
• Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions
• Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains
• Boundary Value Problems, Weyl Functions, and Differential Operators
• The Krein–von Neumann Realization of Perturbed Laplacians on Bounded Lipschitz Domains
• Q-functions and Boundary Triplets of Nonnegative Operators
• 1-D Schr\"odinger operators with local point interactions: a review
• Boundary pairs associated with quadratic forms