Lévy Khinchin Formula on Commutative Hypercomplex System

• Journal title : Kyungpook mathematical journal
• Volume 48, Issue 4,  2008, pp.559-575
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2008.48.4.559
Title & Authors
Lévy Khinchin Formula on Commutative Hypercomplex System
Zabel, Ahmed Moustfa; Dehaish, Buthinah Abdullateef Bin;

Abstract
A commutative hypercomplex system $\small{L_1}$(Q,m) is, roughly speaking, a space which is defined by a structure measure (c(A,B, r), (A,$\small{B{\in}{\beta}}$(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$\small{\$vy measure in the L$\small{\$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$\small{\$vy Khinchin formula;
Language
English
Cited by
1.
Exponentially Convex Functions on Hypercomplex Systems, International Journal of Mathematics and Mathematical Sciences, 2011, 2011, 1
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