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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 σ(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 Δ=[−1,1] with respect to a complex-valued
weight h(x)=σ(x)/√1−x2.
Keywords:
orthogonal polynomials, Padé polynomials, strong asymptotics, Bernshtein's formula, Nuttall's method.
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. Math., 79:6 (2015), 1215–1234
Linking options:
https://www.mathnet.ru/eng/im8374https://doi.org/10.1070/IM2015v079n06ABEH002778 https://www.mathnet.ru/eng/im/v79/i6/p125
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Abstract page: | 696 | Russian version PDF: | 179 | English version PDF: | 31 | References: | 63 | First page: | 18 |
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