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

N. R. Ikonomov ; R. K. Kovacheva ; S. P. Suetin

Izvestiya. Mathematics , Tome 79 (2015) no. 6, pp. 1215-1234.

Résumé

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 $h(x)=\sigma(x)/\sqrt{1-x^2}$.

Détail

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

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