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 $h(x)=\sigma(x)/\sqrt{1-x^2}$.
Fulltext:
PDF file (702 kB)
