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Speaker: Martin Buhmann

Abstract: We study positive and strictly positive definite functions on several regular domains. The list includes the unit ball, conic surface, hyperbolic surface, solid hyperboloid, and simplex. Each of these domains can be embedded in a quadrant of the unit sphere by a distance preserving map, from which we derive a characterization of positive definite, and strictly positive definite, functions for each domain. (Joint work with Yuan Xu.)