Strictly positive definite functions on the unit circle

被引：0

作者：

Sun, XP ^{[1
]}

机构：

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

来源：

MATHEMATICS OF COMPUTATION | 2005年 / 74卷 / 250期

关键词：

strict positive-definiteness; the Kronecker approximation; Weyl's criterion; equidistribution;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study strictly positive definite functions on the unit circle in the Euclidean space of dimension two. We develop several conditions pertaining to the determination of such functions. The major result is obtained by considering the set of real numbers as a vector space over the field of rational numbers and then applying the Kronecker approximation theorem and Weyl's criterion on equidistributions.

引用

页码：709 / 721

页数：13

共 50 条

[31] Norm estimates of interpolation matrices and their inverses associated with strictly positive definite functions
Levesley, J
Luo, Z
Sun, X
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (07) : 2127 - 2134
[32] Scattered data interpolation: Strictly positive definite radial basis/cardinal functions
Kazem, Saeed
Hatam, A.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 394
[33] POSITIVE DEFINITE FUNCTIONS ON THE UNIT SPHERE AND INTEGRALS OF JACOBI POLYNOMIALS
Xu, Yuan
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (05) : 2039 - 2048
[34] A function class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions
Jamel El Kamel
Khaled Mehrez
Positivity, 2018, 22 : 1403 - 1417
[35] A function class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions
El Kamel, Jamel
Mehrez, Khaled
POSITIVITY, 2018, 22 (05) : 1403 - 1417
[36] Strictly positive definite kernels on a product of spheres
Guella, J. C.
Menegatto, V. A.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 435 (01) : 286 - 301
[37] Strictly positive definite kernels on a product of circles
J. C. Guella
V. A. Menegatto
A. P. Peron
Positivity, 2017, 21 : 329 - 342
[38] Strictly positive definite kernels on a product of circles
Guella, J. C.
Menegatto, V. A.
Peron, A. P.
POSITIVITY, 2017, 21 (01) : 329 - 342
[39] ON THE MEASURABILITY OF POSITIVE DEFINITE AND CONDITIONALLY POSITIVE DEFINITE FUNCTIONS
SASVARI, Z
MATHEMATISCHE NACHRICHTEN, 1986, 125 : 239 - 242
[40] ON POSITIVE DEFINITE FUNCTIONS
DEVINATZ, A
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 58 (04) : 478 - 478

← 1 2 3 4 5 →