English

Criterion for the resolvent set of nonsymmetric tridiagonal operators

Classical Analysis and ODEs 2009-09-25 v1

Abstract

We study nonsymmetric tridiagonal operators acting in the Hilbert space 2\ell^2 and describe the spectrum and the resolvent set of such operators in terms of a continued fraction related to the resolvent. In this way we establish a connection between Pad\'e approximants and spectral properties of nonsymmetric tridiagonal operators.

Keywords

Cite

@article{arxiv.math/9401208,
  title  = {Criterion for the resolvent set of nonsymmetric tridiagonal operators},
  author = {A. I. Aptekarev and Valeri\uı A. Kaliaguine and Walter Van Assche},
  journal= {arXiv preprint arXiv:math/9401208},
  year   = {2009}
}