Absolutely continuous Jacobi operators

Author:
Steen Pedersen

Journal:
Proc. Amer. Math. Soc. **130** (2002), 2369-2376

MSC (2000):
Primary 33C45, 39A70; Secondary 47A10, 47B39

Published electronically:
February 4, 2002

MathSciNet review:
1897462

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Abstract: We show (among other results) that a symmetric Jacobi matrix whose diagonal is the zero sequence and whose super-diagonal satisfies , and has purely absolutely continuous spectrum when considered as a self-adjoint operator on .

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Additional Information

**Steen Pedersen**

Affiliation:
Department of Mathematics, Wright State University, Dayton, Ohio 45435

Email:
steen@math.wright.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-02-06339-6

Keywords:
Orthogonal polynomials,
weighted shift,
absolute continuity,
Jacobi matrix

Received by editor(s):
September 1, 2000

Received by editor(s) in revised form:
March 21, 2001

Published electronically:
February 4, 2002

Communicated by:
David R. Larson

Article copyright:
© Copyright 2002
American Mathematical Society