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Asymptotic properties of Sobolev orthogonal polynomials. (English) Zbl 0933.42013

Here, the author gives an up-to-date account on some new tools and ideas, which have appeared recently in the study of the analytic properties of polynomials orthogonal with respect to inner products involving derivatives. Some results on weak asymptotics are given, while the strong outer asymptotics are also derived. Both, discrete and continuous cases are considered and several open problems and conjectures are posed.

MSC:

42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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