Symmetrically Positive Definite Functions

Abstract

<p> In this thesis we study the representation theorems for evenly positive definite functions on Euclidean spaces. A generalization of the concept of evenness on R^n to a concept of symmetry on any locally compact abelian group is given. In addition, a result analogous to the Weil-Povzner-Raikov Theorem is obtained for the representation of symmetrically positive definite functions on locally compact abelian groups.</p>