Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-26T11:07:40.708Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE EXISTENCE OF WKB-TYPE ASYMPTOTICS FOR THE GENERALIZED EIGENVECTORS OF DISCRETE STRING OPERATORS

Published online by Cambridge University Press:  02 February 2004

SERGEI BELOV  and
ALEXEI RYBKIN
SERGEI BELOV
Affiliation:
Department of Mathematical Sciences, University of Alaska Fairbanks, P.O. Box 756660, Fairbanks, AK 99775, USA
ALEXEI RYBKIN
Affiliation:
Department of Mathematical Sciences, University of Alaska Fairbanks, P.O. Box 756660, Fairbanks, AK 99775, USAffavr@uaf.edu
Get access

Abstract

Let $J$ be a Jacobi real symmetric matrix on $l_{2}$ with zero diagonal and non-diagonal entries of the form $\{1+p_{n}\}$. If $p_{n-1}\pm p_{n}=O(n^{-\alpha})$ with some $\alpha>2/3$, then the existence of bounded solutions of $Ju=\lambda u$ is proved for almost every $\lambda\in(-2,2)$ with the WKB-type asymptotic behavior.

Keywords

47B3647B3747B39
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 2 , March 2004 , pp. 241 - 251
Copyright
© The London Mathematical Society 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)