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Criterion for the resolvent set of nonsymmetric tridiagonal operators

Authors: A. I. Aptekarev, V. Kaliaguine and W. Van Assche
Journal: Proc. Amer. Math. Soc. 123 (1995), 2423-2430
MSC: Primary 47B37; Secondary 41A21, 47A05, 47B39
MathSciNet review: 1254830
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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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Keywords: Tridiagonal operators, resolvents, Padé approximation
Article copyright: © Copyright 1995 American Mathematical Society

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