A GENERALIZATION OF FAVARD THEOREM FOR POLYNOMIALS SATISFYING A RECURRENCE RELATION

被引：56

作者：

DURAN, AJ

机构：

[1] Departamento de Análisis Matematico, Universidad de Sevilla, Sevilla, 41080

来源：

JOURNAL OF APPROXIMATION THEORY | 1993年 / 74卷 / 01期

关键词：

D O I：

10.1006/jath.1993.1055

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give the canonical expression for an inner product (delined in P the linear space of real polynomials), for which the set of orthonormal polynomials satisfies a (2N + 1)-term recurrence relation. This result is a generalization of Favard's theorem about orthogonal polynomials and three-term recurrence relations. Also, we characterize these inner products in terms of symmetric operators. Similar results are proved for some kinds of discrete Sobolev inner products. © 1993 Academic Press, Inc.

引用

页码：83 / 109

页数：27

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