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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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