The Moment Problem in Hypercomplex Systems

Hossam Hassan; A. S. Okb El Bab; H. A. Ghany; R.M Boshnaa

doi:10.24297/jam.v10i7.1790

Authors

Hossam Hassan Helwan University, Cairo(11282), Egypt.
A. S. Okb El Bab Helwan University, Cairo(11282), Egypt.
H. A. Ghany Al Azhar University, Cairo, Egypt.
R.M Boshnaa Taif University, Taif(888), Saudi Arabia.

DOI:

https://doi.org/10.24297/jam.v10i7.1790

Keywords:

Hypercomplex, Moment problem, Positive definite.

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) .