Polya-type criteria for conditional strict positive definiteness of functions on spheres

JOURNAL OF APPROXIMATION THEORY

卷:257

Article

Buhmann, Martin¹  Jaeger, Janin¹ 

[1] Justus Liebig Univ, Lehrstuhl Numer Math, D-35392 Giessen, Germany

关键词: Spherical basis functions;    Isotropic kernels;    Dot product kernels;    Completely monotone functions;    Interpolation of scattered data;    Conditionally positive definite kernels;   

DOI  :  10.1016/j.jat.2020.105440

来源: Elsevier

【 摘 要 】

Identifying (conditionally) strictly positive definite functions is of great importance as they allow the unique solution of certain interpolation problems. We introduce new sufficient (and some necessary) conditions for functions to be conditionally strictly positive definite on all spheres Sd-1, d > 2, only employing monotonicity properties. For strictly positive definite and conditionally negative definite functions on all spheres we give a characterisation in terms of monotonicity properties. Further, we prove that multiply monotone functions are positive definite on spheres up to a certain dimension. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free