Zero Distribution of Orthogonal Polynomials in a Certain Discrete Sobolev Space

摘要

The study concerns the zero distribution of the polynomials (in braces: S sub n,sup N) which are orthogonal with respect to the discrete Sobolev inner product = integral from 0 to infinity, of f(x) g(x) d(psi)(x) + N f(sup r)(0)g(sup r)(0), where psi is a distribution function, N =or> 0, r =or> 1. (S sub n, sup N) has n real, simple zeros; at most one of them is outside (0, infinity). The location of these zeros is given in relation to the position of the zeros of some classical polynomials (i.e. polynomials with respect to an inner product with N = 0). (Copyright (c) 1991 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)