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Funktsional'nyi Analiz i ego Prilozheniya, 2007, Volume 41, Issue 2, Pages 44–57
DOI: https://doi.org/10.4213/faa2860 (Mi faa2860) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The Inverse Problem for Krein Orthogonal Matrix Functions

I. Ts. Gokhberga, M. A. Kaashoekb, L. E. Lererc

a Tel Aviv University, School of Mathematical Sciences
b Vrije Universiteit
c Technion – Israel Institute of Technology
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DOI: https://doi.org/10.4213/faa2860
Abstract: In the mid-fifties, in a seminal paper, M. G. Krein introduced continuous analogs of Szegő orthogonal polynomials on the unit circle and established their main properties. In this paper, we generalize these results and subsequent results that he obtained jointly with Langer to the case of matrix-valued functions. Our main theorems are much more involved than their scalar counterparts. They contain new conditions based on Jordan chains and root functions. The proofs require new techniques based on recent results in the theory of continuous analogs of resultant and Bezout matrices and solutions of certain equations in entire matrix functions.
Keywords: Krein orthogonal function, continuous analog of orthogonal polynomials, entire matrix function equation, Jordan chain, root function, inverse problem.
Received: 01.11.2006
English version:
Functional Analysis and Its Applications, 2007, Volume 41, Issue 2, Pages 115–125
DOI: https://doi.org/10.1007/s10688-007-0011-1
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: I. Ts. Gokhberg, M. A. Kaashoek, L. E. Lerer, “The Inverse Problem for Krein Orthogonal Matrix Functions”, Funktsional. Anal. i Prilozhen., 41:2 (2007), 44–57; Funct. Anal. Appl., 41:2 (2007), 115–125
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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