A necessary and sufficient condition for strictly positive definite functions on spheres

被引：94

作者：

Chen, DB ^{[1
]}

Menegatto, VA

Xun, XP

机构：

[1] Oklahoma State Univ, Dept Comp Sci, Tulsa, OK 74106 USA

[2] Univ Sao Paulo, ICMC, BR-13560970 Sao Carlos, SP, Brazil

[3] SW Missouri State Univ, Dept Math, Springfield, MO 65804 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2003年 / 131卷 / 09期

关键词：

strict positive-definiteness; spherical harmonics; Gegenbauer polynomials;

D O I：

10.1090/S0002-9939-03-06730-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a necessary and sufficient condition for the strict positive-definiteness of real and continuous functions on spheres of dimension greater than one.

引用

页码：2733 / 2740

页数：8

共 11 条

[1]

ASKEY R, 1975, REGIONAL C SER APPL, V21

[2]

MENEGATOO VA, 1994, APPL ANAL, V55, P81

[3] STRICTLY POSITIVE-DEFINITE KERNELS ON THE CIRCLE [J].

MENEGATTO, VA .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1995, 25 (03) :1149-1163

[4]

MENEGATTO VA, 1992, THESIS U TEXAS AUSTI

[5] Strictly positive definite functions on spheres in Euclidean spaces [J].

Ron, A ;

Sun, XP .

MATHEMATICS OF COMPUTATION, 1996, 65 (216) :1513-1530

[6]

RON A, 1994, 946 CMS TR U WISC MA

[7]

SCHOENBERG I. J., 1942, Duke Math. J., V9, P96

[8] On a new condition for strictly positive definite functions on spheres [J].

Schreiner, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (02) :531-539

[9]

Stein E.M., 1971, Princeton Math. Ser., V32

[10]

SZEGO G, 1959, AM MATH C PUBL, V23

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