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Lévy Khinchin Formula on Commutative Hypercomplex System
Zabel, Ahmed Moustfa,Dehaish, Buthinah Abdullateef Bin Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.4
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.
Negative Definite Functions on Hypercomplex Systems
Zabel, Ahmed M.,Dehaish, Buthinah A. Bin Department of Mathematics 2006 Kyungpook mathematical journal Vol.46 No.2
We present a concept of negative definite functions on a commutative normal hypercomplex system $L_1$(Q, $m$) with basis unity. Negative definite functions were studied in [5] and [4] for commutative groups and semigroups respectively. The definition of such functions on Q is a natural generalization of that defined on a commutative hypergroups.