2022/04/12 by Buhmann, Martin, Xu, Yuan
#33B10 #41A05 #41A63 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2204.05696
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.