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On time-dependent orthogonal polynomials on the unit circle

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Abstract

Two index formulas for operators defined by infinite band matrices are proved. These results may be interpreted as a generalization of a classical theorem of M. G. Krein on orthogonal polynomials. The proofs are based on dichotomy and nonstationary inertia theory.

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Authors and Affiliations

  1. School of Mathematical Sciences, Raymond and Beverly Sacker Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Asher Ben-Artzi & Israel Gohberg

Authors
  1. Asher Ben-Artzi
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  2. Israel Gohberg
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Additional information

Dedicated to the memory of M. G. Krein, a mathematical giant, a great teacher and wonderful friend.

Published in Ukrainskii Matematicheskii Zhurnal, Vol. 46, Nos. 1–2, pp. 18–36, January–February, 1994.

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Ben-Artzi, A., Gohberg, I. On time-dependent orthogonal polynomials on the unit circle. Ukr Math J 46, 15–33 (1994). https://doi.org/10.1007/BF01056998

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  • DOI: https://doi.org/10.1007/BF01056998

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