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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
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
Citation:
L. B. Golinskii, “Schur flows and orthogonal polynomials on the unit circle”, Sb. Math., 197:8 (2006), 1145–1165
Linking options:
https://www.mathnet.ru/eng/sm1488https://doi.org/10.1070/SM2006v197n08ABEH003792 https://www.mathnet.ru/eng/sm/v197/i8/p41
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Abstract page: | 521 | Russian version PDF: | 227 | English version PDF: | 22 | References: | 55 | First page: | 4 |
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