Abstract
The theorem of Krein, concerning the location of the zeros of orthogonal polynomials in an indefinite metric, is extended to the nonstationary block case. The proof relies heavily on results concerning nonstationary Stein equations and dichotomy from the authors’ paper [2] and [3].
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References
D. Alpay and I. Gohberg, On Orthogonal Matrix Polynomials, this volume.
A. Ben-Artzi and I. Gohberg, Inertia Theorems for Nonstationary Discrete Systems and Dichotomy, to appear in Linear Algebra and its Applications.
A. Ben-Artzi and I. Gohberg, Fredholm Properties of Band Matrices and Dichotomy. Operator Theory: Advances and Applications, Vol. 32, Topics in Operator Theory. Constantin Apostol Memorial Issue, Birkhauser Verlag, 1988.
I. Gohberg and L. Lerer, Matrix Generalizations of M.G. Krein Theorems on Orthogonal Polynomials, this volume.
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© 1988 Springer Basel AG
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Ben-Artzi, A., Gohberg, I. (1988). Extension of a Theorem of M. G. Krein on Orthogonal Polynomials for the Nonstationary Case. In: Gohberg, I. (eds) Orthogonal Matrix-valued Polynomials and Applications. Operator Theory: Advances and Applications, vol 34. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5472-6_4
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DOI: https://doi.org/10.1007/978-3-0348-5472-6_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5474-0
Online ISBN: 978-3-0348-5472-6
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