The abstract inverse scattering problem and the instability of completeness of orthogonal systems

DOI10.1016/0022-1236(88)90010-9zbMath0663.47008OpenAlexW2082946983MaRDI QIDQ1114138

Sergei Khrushchev

Publication date: 1988

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(88)90010-9

zbMATH Keywords

scattering operatorunitary operatorsorthogonal systemsabstract inverse scattering problemcontractive operator-valued functionWeyl's criterion of essential not left invertibility

Mathematics Subject Classification ID

Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Scattering theory of linear operators (47A40)

Cites Work

• The Taylor coefficients of inner functions
• Discrete time systems, operator models, and scattering theory
• Large and small subspaces of Hilbert space
• The singular spectrum of the weakly perturbed multiplication operator
• Characterizations of measures whose Fourier-Stieltjes transforms vanish at infinity
• Dilation theory and spectral analysis of nonselfadjoint differential operators
• On unitary couplings of semiunitary operators
• Scattering theory
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