Selfadjoint \(\Pi _{\kappa}\)-extensions of symmetric subspaces: An abstract approach to boundary problems with spectral parameter in the boundary conditions

DOI10.1007/BF01238863zbMath0552.47014MaRDI QIDQ801524

Aalt Dijksma, Hendrik S. V. de Snoo, Heinz K. Langer

Publication date: 1984

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

generalized resolventPontryagin spaceselfadjoint subspaceboundary problems with spectral parameter in the boundary conditionsclasses of meromorphic, operator or subspace valued mappingscompressed resolventsformally symmetric ordinary differential expressionsŠtraus extensionsŠtraus manifolds

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Linear differential equations in abstract spaces (34G10) Linear operators on spaces with an indefinite metric (47B50)

Related Items (16)

The theory of V-Bézoutians and its applications ⋮ Symmetric and Isometric Relations ⋮ Schur Analysis in an Indefinite Setting ⋮ Selfadjoint extensions of symmetric operators in degenerated inner product spaces ⋮ Basis properties in \({L}_{p}\) of root functions of Sturm-Liouville problem with spectral parameter-dependent boundary conditions ⋮ Compressions of maximal dissipative and self-adjoint linear relations and of dilations ⋮ An expansion theorem for regular elliptic eigenvalue problem with eigenvalue parameter in the boundary conditions. ⋮ Linearization of boundary eigenvalue problems ⋮ A Schur transformation for functions in a general class of domains ⋮ Boundary eigenvalue problems for differential equations \(N\eta=\lambda P\eta\) with \(\lambda\)-polynomial boundary conditions ⋮ The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces ⋮ Selfadjoint extensions of regular canonical systems with Stieltjes boundary conditions ⋮ Generalized resolvent matrices and spaces of analytic functions ⋮ Singular point-like perturbations of the Bessel operator in a Pontryagin space ⋮ On Some Class of Self-adjoint Boundary Value Problems with the Spectral Parameter in the Equations and the Boundary Conditions ⋮ Reflectionless potentials and point interactions in Pontryagin spaces

Cites Work

• L-resolvent matrices of symmetric linear relations with equal defect numbers; applications to canonical differential relations
• Self-adjoint extensions of symmetric subspaces
• On generalized resolvents and \(Q\)-functions of symmetric linear relations (subspaces) in Hilbert space
• Operator treatment of boundary problems with spectral parameters entering via polynomials in the boundary conditions
• Spectral measures, generalized resolvents, and functions of positive type
• Resolvent matrix of Hermitian operator and the characteristic functions related to it
• Self-adjoint subspace extensions satisfying λ-linear boundary conditions
• Eigenfunction expansions for a class of J-selfadjoint ordinary differential operators with boundary conditions containing the eigenvalue parameter
• Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions
• Extensions of isometric and symmetric linear relations in a Krein space
• Generalized Resolvents of Ordinary Differential Operators
• EXTENSIONS AND GENERALIZED RESOLVENTS OF A SYMMETRIC OPERATOR WHICH IS NOT DENSELY DEFINED
• Defect subspaces and generalized resolvents of an Hermitian operator in the space \(\Pi_\kappa\)
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