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Mat. Sb., 2014, Volume 205, Number 9, Pages 121–144 (Mi msb8360)  

This article is cited in 4 scientific papers (total in 4 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

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 $e_1<e_2<…<e_{2p}$, $Q(x)=x^{2m}+\dotsb$ 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

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8360

Full text: PDF file (678 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:9, 1334–1356

Bibliographic databases:

UDC: 517.53
Received: 17.03.2014 and 23.06.2014

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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\vol 205
\issue 9
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  • https://doi.org/10.4213/sm8360
  • http://mi.mathnet.ru/eng/msb/v205/i9/p121

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    This publication is cited in the following articles:
    1. V. I. Buslaev, S. P. Suetin, “On equilibrium problems related to the distribution of zeros of the Hermite–Padé polynomials”, Proc. Steklov Inst. Math., 290:1 (2015), 256–263  mathnet  crossref  crossref  isi  elib  elib
    2. S. P. Suetin, “Distribution of the zeros of Padé polynomials and analytic continuation”, Russian Math. Surveys, 70:5 (2015), 901–951  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. N. R. Ikonomov, R. K. Kovacheva, S. P. Suetin, “Nuttall's integral equation and Bernshtein's asymptotic formula for a complex weight”, Izv. Math., 79:6 (2015), 1215–1234  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    4. E. Levin, D. Lubinsky, Bounds and asymptotics for orthogonal polynomials for varying weights, Springerbriefs in Mathematics, Springer, 2018  crossref  mathscinet  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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