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Izvestiya: Mathematics, 2015, Volume 79, Issue 6, Pages 1215–1234
DOI: https://doi.org/10.1070/IM2015v079n06ABEH002778 (Mi im8374) 		 
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
English version PDF (392 kB) Citations (1)
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DOI: https://doi.org/10.1070/IM2015v079n06ABEH002778
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).
Received: 01.04.2015
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2015, Volume 79, Issue 6, Pages 125–144
DOI: https://doi.org/10.4213/im8374
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 30B70, 33D45, 41A21, 41A25, 41A60, 42C05
Language: English
Original paper language: Russian
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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\paper Nuttall's integral equation and Bernshtein's asymptotic formula for a~complex weight
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\pages 125--144
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  • https://www.mathnet.ru/eng/im/v79/i6/p125
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:56
    First page:18
     
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