Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

Details Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

2006-04-04

arxiv.org/abs/math/0604074v2

Mathematics

Classical Analysis and ODEs

Changed content; 34 pages, 41 references

Scientific paper

10.1007/s10440-006-9073-y

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some new directions for a future research are formulated.

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