Criterion for the resolvent set of nonsymmetric tridiagonal operators

Details Criterion for the resolvent set of nonsymmetric tridiagonal operators Criterion for the resolvent set of nonsymmetric tridiagonal operators

1994-01-21

arxiv.org/abs/math/9401208v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We study nonsymmetric tridiagonal operators acting in the Hilbert space
$\ell^2$ 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.

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