Positive Definite and Related Functions in the Product of Hypercomplex Systems (Global Journal of Science Frontier Research, 2017)
The main aim of this paper is to explore harmonic properties of functions defined in the product of hypercomplex systems. By means of the generalized translation operators, the precise definition of the product of commutative hypercomplex systems is given and full description for its properties are shown. The integral representations of positive definite function defined in the product of commutative normal hypercomplex systems are given. Furthermore, we present the necessary and sufficient conditions guarantees the property of positive definite function in the product of hypercomplex systems.
Keywords: hypercomplex systems; generalized translation operators; direct product; positive definite