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

被引：89

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 50 条

[1] On a new condition for strictly positive definite functions on spheres
Schreiner, M
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (02) : 531 - 539
[2] STRICTLY POSITIVE DEFINITE FUNCTIONS ON SPHERES
XU, Y
CHENEY, EW
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 116 (04) : 977 - 981
[3] Strictly and non-strictly positive definite functions on spheres
Gneiting, Tilmann
[J]. BERNOULLI, 2013, 19 (04) : 1327 - 1349
[4] Strictly positive definite multivariate covariance functions on spheres
Guella, Jean Carlo
Menegatto, Valdir Antonio
Porcu, Emilio
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2018, 166 : 150 - 159
[5] Strictly positive definite functions on spheres in Euclidean spaces
Ron, A
Sun, XP
[J]. MATHEMATICS OF COMPUTATION, 1996, 65 (216) : 1513 - 1530
[6] Necessary and sufficient condition of complex positive definite matrices
Yuan, Hui-ping
Li, Qing-yu
[J]. Advances in Matrix Theory and Applications, 2006, : 339 - 342
[7] On the conditioning of interpolation by strictly conditionally positive definite functions on spheres
Luo, Z
Levesley, J
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1998, 19 (7-8) : 849 - 871
[8] Strictly positive definite functions
Chang, KF
[J]. JOURNAL OF APPROXIMATION THEORY, 1996, 87 (02) : 148 - 158
[9] Strictly positive definite kernels on a product of spheres
Guella, J. C.
Menegatto, V. A.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 435 (01) : 286 - 301
[10] Dimension hopping and families of strictly positive definite zonal basis functions on spheres
Beatson, R. K.
Castell, W. Zu
[J]. JOURNAL OF APPROXIMATION THEORY, 2017, 221 : 22 - 37

← 1 2 3 4 5 →