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Sbornik: Mathematics, 2004, Volume 195, Issue 11, Pages 1639–1663
DOI: https://doi.org/10.1070/SM2004v195n11ABEH000860
(Mi sm860)
 

This article is cited in 10 scientific papers (total in 10 papers)

Circular parameters of polynomials orthogonal on several arcs of the unit circle

A. L. Lukashov

Saratov State University named after N. G. Chernyshevsky
References:
Abstract: The asymptotic behaviour of the circular parameters $(a_n)$ of the polynomials orthogonal on the unit circle with respect to Geronimus measures is analysed. It is shown that only when the harmonic measures of the arcs making up the support of the orthogonality measure are rational do the corresponding parameters form a pseudoperiodic sequence starting from some index (that is, after a suitable rotation of the circle and the corresponding modification of the orthogonality measures they form a periodic sequence). In addition it is demonstrated that if the harmonic measures of these arcs are linearly independent over the field of rational numbers, then the sets of limit points of the sequences of absolute values of the circular parameters $|a_n|$ and of their ratios $(a_{n+k}/a_n)_{n=1}^\infty$ are a closed interval on the real line and a continuum in the complex plane, respectively.
Received: 25.12.2001 and 09.02.2004
Bibliographic databases:
UDC: 517.5
MSC: Primary 42C05; Secondary 30F35
Language: English
Original paper language: Russian
Citation: A. L. Lukashov, “Circular parameters of polynomials orthogonal on several arcs of the unit circle”, Sb. Math., 195:11 (2004), 1639–1663
Citation in format AMSBIB
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\by A.~L.~Lukashov
\paper Circular parameters of polynomials orthogonal on several arcs of the unit circle
\jour Sb. Math.
\yr 2004
\vol 195
\issue 11
\pages 1639--1663
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  • https://doi.org/10.1070/SM2004v195n11ABEH000860
  • https://www.mathnet.ru/eng/sm/v195/i11/p95
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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