GENERAL SOBOLEV ORTHOGONAL POLYNOMIALS

Authors
MARCELLAN F PEREZ TE PINAR MA RONVEAUX A
Citation
F. Marcellan et al., GENERAL SOBOLEV ORTHOGONAL POLYNOMIALS, Journal of mathematical analysis and applications, 200(3), 1996, pp. 614-634
Citations number
18
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics,Mathematics
Journal title
Journal of mathematical analysis and applications → ACNP
ISSN journal
0022247X
Volume
200
Issue
3
Year of publication
1996
Pages
614 - 634
Database
ISI
SICI code
0022-247X(1996)200:3<614:GSOP>2.0.ZU;2-A
Abstract
In this paper, we study orthogonal polynomials with respect to the inn er product (f, g)(S)((N)) = [u, fg] + Sigma(m=1)(N) lambda(m)[u, f((m) )g((m))], where lambda(m) greater than or equal to 0 for m = 1,..., N, and u is a semiclassical, positive definite linear functional. For th ese non-standard orthogonal polynomials, algebraic and differential pr operties are obtained, as well as their representation in terms of the standard orthogonal polynomials associated with u. (C) 1996 Academic Press, Inc.