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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 6, Pages 125–144 (Mi izv8374)  

This article is cited in 1 scientific paper (total in 1 paper)

Nuttall's integral equation and Bernshtein's asymptotic formula for a complex weight

N. R. Ikonomova, R. K. Kovachevaa, S. P. Suetinb

a Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
b Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: We obtain Nuttall's integral equation provided that the corresponding complex-valued function $\sigma(x)$ does not vanish and belongs to the Dini–Lipschitz class. Using this equation, we obtain a complex analogue of Bernshtein's classical asymptotic formulae for polynomials orthogonal on the closed unit interval $\Delta=[-1,1]$ with respect to a complex-valued weight $h(x)=\sigma(x)/\sqrt{1-x^2}$.

Keywords: orthogonal polynomials, Padé polynomials, strong asymptotics, Bernshtein's formula, Nuttall's method.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-12430-офи-м-2
15-01-07531-a
Ministry of Education and Science of the Russian Federation НШ-2900.2014.1
This paper was written with the financial support of the RFBR (grants nos. 13-01-12430-ofi-m-2, 15-01-07531-a) and the President's Programme ‘Support of Leading Scientific Schools’ (grant no. NSh-2900.2014.1).


DOI: https://doi.org/10.4213/im8374

Full text: PDF file (702 kB)
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English version:
Izvestiya: Mathematics, 2015, 79:6, 1215–1234

Bibliographic databases:

UDC: 517.53
MSC: 30B70, 33D45, 41A21, 41A25, 41A60, 42C05
Received: 01.04.2015

Citation: N. R. Ikonomov, R. K. Kovacheva, S. P. Suetin, “Nuttall's integral equation and Bernshtein's asymptotic formula for a complex weight”, Izv. RAN. Ser. Mat., 79:6 (2015), 125–144; Izv. Math., 79:6 (2015), 1215–1234

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. V. Komlov, R. V. Palvelev, S. P. Suetin, E. M. Chirka, “Hermite–Padé approximants for meromorphic functions on a compact Riemann surface”, Russian Math. Surveys, 72:4 (2017), 671–706  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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