Compressions of self-adjoint extensions of a symmetric operator and M.G. Krein's resolvent formula

DOI10.1007/s00020-018-2465-3OpenAlexW2805372510WikidataQ124629958 ScholiaQ124629958MaRDI QIDQ1790639

Aalt Dijksma, Heinz K. Langer

Publication date: 2 October 2018

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

Full work available at URL: https://doi.org/10.1007/s00020-018-2465-3

zbMATH Keywords

Hilbert spacecompressiongeneralized resolventKrein's resolvent formulaself-adjoint extension\(Q\)-functionsymmetric and self-adjoint operators

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Dilations, extensions, compressions of linear operators (47A20)

Related Items (8)

On uniform convergence of the inverse Fourier transform for differential equations and Hamiltonian systems with degenerating weight ⋮ On compressions of self-adjoint extensions of a symmetric linear relation ⋮ On compressions of self-adjoint extensions of a symmetric linear relation with unequal deficiency indices ⋮ Self-Adjoint Extensions of a Symmetric Linear Relation with Finite Defect: Compressions and Straus Subspaces ⋮ Compressed resolvents, Schur functions, Nevanlinna families and their transformations ⋮ On couplings of symmetric operators with possibly unequal and infinite deficiency indices ⋮ W. Stenger's and M. A. Nudelman's results and resolvent formulas involving compressions ⋮ The A-model with mutually equal model parameters can lead to a Hilbert space model

Cites Work

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• Closedness and adjoints of products of operators, and compressions
• Compressions of maximal dissipative and self-adjoint linear relations and of dilations
• On Matrix-Valued Herglotz Functions
• Finite-dimensional Self-adjoint Extensions of a Symmetric Operator with Finite Defect and their Compressions
• Realization of nonstrict matrix Nevanlinna functions as Weyl functions of symmetric operators in Pontryagin spaces
• On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space
• On the projection of a selfadjoint operator
• Extension theory of formally normal and symmetric subspaces
• Defect subspaces and generalized resolvents of an Hermitian operator in the space \(\Pi_\kappa\)
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