Positive definite functions on a regular domain
Classical Analysis and ODEs
2024-01-02 v3 Numerical Analysis
Numerical Analysis
Abstract
We define positive and strictly positive definite functions on a domain and study these functions on a list of regular domains. The list includes the unit ball, conic surface, hyperbolic surface, solid hyperboloid, and simplex. Each of these domains is embedded in a quadrant or a union of quadrants of the unit sphere by a distance preserving map, from which characterizations of positive definite and strictly positive definite functions are derived for these regular domains.
Cite
@article{arxiv.2204.05696,
title = {Positive definite functions on a regular domain},
author = {Martin Buhmann and Yuan Xu},
journal= {arXiv preprint arXiv:2204.05696},
year = {2024}
}