The Moment Problem in Hypercomplex Systems

Abstract

This paper is devoted to give the necessary and sufficient conditions guarantees that the product of two generalized moment functions defined in a hypercomplex system L₁(Q,m) is also generalized moment function in L₁(Q,m) . Also, we prove that a bounded continuous function  in a hypercomplex system L₁(Q,m) is conditionally positive definite if and only if is generalized moment functions defined in L₁(Q,m) . Moreover, we will give the integral representations of a generalized moment functions defined in L₁ (Q, m) .