# Lévy Khinchin Formula on Commutative Hypercomplex System

Zabel, Ahmed Moustfa;Dehaish, Buthinah Abdullateef Bin

• Published : 2008.12.31
• 20 4

#### Abstract

A commutative hypercomplex system $L_1$(Q,m) is, roughly speaking, a space which is defined by a structure measure (c(A,B, r), (A,$B{\in}{\beta}$(Q)). Such space has bee studied by Berezanskii and Krein. Our main purpose is to establish a generalization of convolution semigroups and to discuss the role of the L$\'{e}$vy measure in the L$\'{e}$vy-Khinchin representation in terms of continuous negative definite functions on the dual hypercomplex system.

#### Keywords

Hypercomplex system;positive and negative definite functions;convolution semigroup;L$\'{e}$vy Khinchin formula

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#### Cited by

1. Exponentially Convex Functions on Hypercomplex Systems vol.2011, 2011, https://doi.org/10.1155/2011/290403