On linearly related orthogonal polynomials and their functionals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:287

Article

Alfaro, M ; Marcellán, F ; Peña, A ; Rezola, ML

关键词: orthogonal polynomials;    recurrence relations;    linear functionals;   

DOI  :  10.1016/S0022-247X(03)00565-1

来源: Elsevier

【 摘 要 】

Let {P-n} be a sequence of polynomials orthogonal with respect a linear functional u and {Q(n)} a sequence of polynomials defined by P-n (x) + s(n) Pn-1 (x) = Q(n) (x) + t(n)Q(n-1) (x). We find necessary and sufficient conditions in order to {Q(n)} be a sequence of polynomials orthogonal with respect to a linear functional nu. Furthermore we prove that the relation between these linear functionals is (x - (a) over tilde )u = lambda(x - a)nu. Even more, if u and nu are linked in this way we get that {P-n} and {Q(n)} satisfy a formula as above. (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

Free