Pairs of selfadjoint operators and their invariants

DOI10.1090/S1061-0022-04-00844-1zbMath1084.47019OpenAlexW1914040905MaRDI QIDQ4675546

Israel Gohberg, Daniel Alpay

Publication date: 4 May 2005

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-04-00844-1

zbMATH Keywords

trace formulaWeyl functioncharacteristicpairs of self-adjoint operators\(Q\)-function associated with a symmetric operatorKreĭn's spectral shift function

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) Inverse scattering problems in quantum theory (81U40) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (3)

Generalized \(Q\)-functions and Dirichlet-to-Neumann maps for elliptic differential operators ⋮ Partially fundamentally reducible operators in Kreĭn spaces ⋮ Realizations of slice hyperholomorphic generalized contractive and positive functions

Cites Work

• Hilbert spaces of analytic functions, inverse scattering and operator models. II
• Factorization of matrix and operator functions. The state space method
• Matrices and indefinite scalar products
• On generalized resolvents and \(Q\)-functions of symmetric linear relations (subspaces) in Hilbert space
• A trace formula for canonical differential expressions.
• Inverse spectral problem for differential operators with rational scattering matrix functions
• Self-adjoint operators and pairs of Hermitian forms over the quaternions
• A supplement to the paper on exponential representations of analytic functions in the upper half-plane with positive imaginary part
• A relationship between the Nehari and the Carathéodory-Toeplitz extension problems
• A unitary invariant for pairs of self-adjoint operators.
• Perturbations of Self-Adjoint Transformation
• Theory of Reproducing Kernels
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