Cyclic operators, commutators, and absolutely continuous measures

Author:

Dombrowski J.

Abstract

Commutator equations are used to study the relationship between the tridiagonal matrix structure of an unbounded cyclic selfadjoint operator and its spectrum. Sufficient conditions are given for absolute continuity. Results are related to the study of systems of orthogonal polyomials for which the measure of orthogonality is supported on an unbounded subset of the real line.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference6 articles.

1. Tridiagonal matrix representations of cyclic selfadjoint operators;Dombrowski, Joanne;Pacific J. Math.,1984

2. Tridiagonal matrix representations of cyclic selfadjoint operators. II;Dombrowski, J.;Pacific J. Math.,1985

3. Orthogonal polynomials and absolutely continuous measures;Máté, Attila,1983

4. Orthogonal polynomials;Nevai, Paul G.;Mem. Amer. Math. Soc.,1979

5. C. R. Putnam, Commutation properties of Hilbert space operators and related topics, Ergebnisse der Math., No. 36, Springer, 1967.

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