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Absolutely continuous Jacobi operators


Author: Steen Pedersen
Journal: Proc. Amer. Math. Soc. 130 (2002), 2369-2376
MSC (2000): Primary 33C45, 39A70; Secondary 47A10, 47B39
DOI: https://doi.org/10.1090/S0002-9939-02-06339-6
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 $h_n>0$satisfies $h_{2n-1}=h_{2n}$, $h_k\leq h_{k+1}$ and $0<b\leq\tfrac{h_{2k+2}}{k+1}\leq\tfrac{h_{2k}}{k}$ has purely absolutely continuous spectrum when considered as a self-adjoint operator on $\ell^2(\mathbb{N} )$.


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Additional Information

Steen Pedersen
Affiliation: Department of Mathematics, Wright State University, Dayton, Ohio 45435
Email: steen@math.wright.edu

DOI: https://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

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