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Sbornik: Mathematics, 2014, Volume 205, Issue 9, Pages 1334–1356
DOI: https://doi.org/10.1070/SM2014v205n09ABEH004420
(Mi sm8360)
 

This article is cited in 5 scientific papers (total in 5 papers)

An asymptotic formula for polynomials orthonormal with respect to a varying weight. II

A. V. Komlov, S. P. Suetin

Steklov Mathematical Institute of Russian Academy of Sciences
References:
Abstract: This paper gives a proof of the theorem announced by the authors in the preceding paper with the same title. The theorem states that asymptotically the behaviour of the polynomials which are orthonormal with respect to the varying weight $e^{-2nQ(x)}p_g(x)/\sqrt{\prod_{j=1}^{2p}(x-e_j)}$ coincides with the asymptotic behaviour of the Nuttall psi-function, which solves a special boundary-value problem on the relevant hyperelliptic Riemann surface of genus $g=p-1$. Here $e_1<e_2<\dots<e_{2p}$, $Q(x)=x^{2m}+\dotsb$ is a monic polynomial of even degree $2m$ and $p_g$ is a certain auxiliary polynomial of degree $p-1$.
Bibliography: 23 titles.
Keywords: varying weight, orthonormal polynomials, strong asymptotics, uniform distributions.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-12430-офи-м2
13-01-00622-а
14-01-31281-мол-а
Ministry of Education and Science of the Russian Federation НШ-2900.2014.1
Received: 17.03.2014 and 23.06.2014
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 9, Pages 121–144
DOI: https://doi.org/10.4213/sm8360
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: English
Original paper language: Russian
Citation: A. V. Komlov, S. P. Suetin, “An asymptotic formula for polynomials orthonormal with respect to a varying weight. II”, Mat. Sb., 205:9 (2014), 121–144; Sb. Math., 205:9 (2014), 1334–1356
Citation in format AMSBIB
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\by A.~V.~Komlov, S.~P.~Suetin
\paper An asymptotic formula for polynomials orthonormal with respect to a~varying weight.~II
\jour Mat. Sb.
\yr 2014
\vol 205
\issue 9
\pages 121--144
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\jour Sb. Math.
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\vol 205
\issue 9
\pages 1334--1356
\crossref{https://doi.org/10.1070/SM2014v205n09ABEH004420}
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  • https://www.mathnet.ru/eng/sm8360
  • https://doi.org/10.1070/SM2014v205n09ABEH004420
  • https://www.mathnet.ru/eng/sm/v205/i9/p121
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    This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:526
    Russian version PDF:240
    English version PDF:14
    References:53
    First page:20
     
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