The Moment Problem in Hypercomplex Systems - Hassan, Hossam; El Bab, A. S. Okb; Ghany, H. A.; Boshnaa, R.M (JOURNAL OF ADVANCES IN MATHEMATICS, 2015)
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) .