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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
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.
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
Linking options:
https://www.mathnet.ru/eng/sm8360https://doi.org/10.1070/SM2014v205n09ABEH004420 https://www.mathnet.ru/eng/sm/v205/i9/p121
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Abstract page: | 526 | Russian version PDF: | 240 | English version PDF: | 14 | References: | 53 | First page: | 20 |
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