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
收藏
页码：83 / 109
页数：27
相关论文
共 14 条
[11]  
KOEKOEK R, 1990, THESIS DELFT U TECHN
[12]   RELATIVE ASYMPTOTICS FOR ORTHOGONAL POLYNOMIALS WITH A SOBOLEV INNER PRODUCT [J].
MARCELLAN, F ;
VANASSCHE, W .
JOURNAL OF APPROXIMATION THEORY, 1993, 72 (02) :193-209
[13]   ON A CLASS OF POLYNOMIALS ORTHOGONAL WITH RESPECT TO A DISCRETE SOBOLEV INNER PRODUCT [J].
MARCELLAN, F ;
RONVEAUX, A .
INDAGATIONES MATHEMATICAE-NEW SERIES, 1990, 1 (04) :451-464
[14]  
Widder DV, 1946, PRINCETON MATH SERIE, V6, P42
12