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Sbornik: Mathematics, 2006, Volume 197, Issue 8, Pages 1145–1165
DOI: https://doi.org/10.1070/SM2006v197n08ABEH003792 (Mi sm1488) 		 
This article is cited in 30 scientific papers (total in 30 papers)

Schur flows and orthogonal polynomials on the unit circle

L. B. Golinskii

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
English version PDF (330 kB) Citations (30)
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DOI: https://doi.org/10.1070/SM2006v197n08ABEH003792
Abstract: Connections between Toda lattices (Toda chains) and similar non-linear chains and the theory of orthogonal polynomials on the real axis have been studied in detail during the last decades. Another system of difference differential equations, known as the Schur flow, is considered in this paper in the framework of the theory of orthogonal polynomials on the unit circle. A Lax pair for this system is found and the dynamics of the corresponding spectral measure is described. The general result is illustrated by an example of Bessel modified measures on the unit circle: the large-time asymptotic behaviour of their reflection coefficients is determined.
Bibliography: 23 titles.
Received: 29.12.2005
Russian version:
Matematicheskii Sbornik, 2006, Volume 197, Number 8, Pages 41–62
DOI: https://doi.org/10.4213/sm1488
Bibliographic databases:
UDC: 517.53+517.91
MSC: 37K10, 33C47
Language: English
Original paper language: Russian
Citation: L. B. Golinskii, “Schur flows and orthogonal polynomials on the unit circle”, Mat. Sb., 197:8 (2006), 41–62; Sb. Math., 197:8 (2006), 1145–1165
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2006v197n08ABEH003792
  • https://www.mathnet.ru/eng/sm/v197/i8/p41
    • This publication is cited in the following 30 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:494
    Russian version PDF:215
    English version PDF:14
    References:48
    First page:4
     
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