Cyclic Operators, Commutators, and Absolutely Continuous Measures

DOI10.2307/2046429zbMath0721.47030OpenAlexW2095069234MaRDI QIDQ5753074

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Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2046429

zbMATH Keywords

orthonormal basisspectral measureseparable Hilbert spaceselfadjointcyclic operatorcommutator equationsabsolutely continuous measures

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Commutators, derivations, elementary operators, etc. (47B47) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37)

Related Items (19)

Spectral analysis of selfadjoint Jacobi matrices with periodically modulated entries ⋮ On one condition of absolutely continuous spectrum for self-adjoint operators and its applications ⋮ Orthogonal polynomials, spectral measures, and absolute continuity ⋮ Spectral measures corresponding to orthogonal polynomials with unbounded recurrence coefficients ⋮ A commutator approach to absolute continuity for unbounded Jacobi operators ⋮ The one-quarter class of orthogonal polynomials ⋮ Absolutely continuous measures for systems of orthogonal polynomials with unbounded recurrence coefficients ⋮ Commuting family of block Jacobi matrices ⋮ Spectral properties of unbounded Jacobi matrices with almost monotonic weights ⋮ Spectral theory of certain unbounded Jacobi matrices ⋮ Unbounded Commuting Operators and Multivariate Orthogonal Polynomials ⋮ On unbounded commuting Jacobi operators and some related issues ⋮ Ted Chihara and his work on orthogonal polynomials ⋮ Spectral theory of a class of block Jacobi matrices and applications ⋮ Inverse spectral problem for Jacobi operators and Miura transformation ⋮ Singular spectrum and recent results on hierarchical operators ⋮ Mourre's theory for some unbounded Jacobi matrices ⋮ Jacobi matrices with power-like weights -- grouping in blocks approach ⋮ Alternative approaches to the absolute continuity of Jacobi matrices with monotonic weights.

Cites Work

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• Tridiagonal matrix representations of cyclic self-adjoint operators
• Tridiagonal matrix representations of cyclic self-adjoint operators. II
• Orthogonal polynomials

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