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Criterion for the resolvent set of nonsymmetric tridiagonal operators

A. I. Aptekarev·Valeri\uı A. Kaliaguine·Walter Van Assche
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Abstract

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 Padé approximants and spectral properties of nonsymmetric tridiagonal operators.

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A. I. Aptekarev, Valeri\uı A. Kaliaguine, Walter Van Assche. 1994-01-21. Criterion for the resolvent set of nonsymmetric tridiagonal operators. https://arxiv.org/abs/math/9401208

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