The extension of positive definite operator-valued functions defined on a symmetric interval of an ordered group

摘要

Let G(1) be an ordered abelian group and a is an element of G(1). Let G(2) be an abelian group and f an operator-valued positive definite function on (-a, a) x G(2). We prove that f admits a positive definite extension to G(1) x G(2), generalizing in this way existing results for the case when G(1) = R and f is continuous. [References: 18]