Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $\ell^2(\mathbb{N} )$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 33C45, 39A70, 47A10, 47B39

Retrieve articles in all journals with MSC (2000): 33C45, 39A70, 47A10, 47B39


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
PII: S 0002-9939(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