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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.
INTEGRAL REPRESENTATION OF GENERALIZED INVARIANT REFLECTION POSITIVE MATRIX KERNEL
Zabel, A.M. Department of Mathematics 1988 Kyungpook mathematical journal Vol.28 No.2
Using the method of eigenfunction expantion of self adjoint operators, we establish the necessary and sufficient conditions for a reflection positive generalized matrix kernel to be represented in an integral form. This integral converges in the cosidered spaces.
The Extension Problem for Exponentially Convex Functions
A. M. Zabel ... et al KYUNGPOOK UNIVERSITY 2003 Kyungpook mathematical journal Vol.43 No.3
Our main result is to prove that every exponentially convex function dened on an open nonempty connected subset of a connected Lie group G can be extended to an exponentially convex function on all G.
The Extension Problem for Exponentially Convex Functions
A. M. Zabel,Maha A. Bajnaid 경북대학교 자연과학대학 수학과 2004 Kyungpook mathematical journal Vol.44 No.1
Our main result is to prove that every exponentially convex function dened on an open nonempty connected subset of a connected Lie group G can be extended to an exponentially convex function on all G.
Extensing of Exponentially Convex Function on the Heisenberg Group
Zabel, A.M.,Bajnaid, Maha A. Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.4
The main purpose of this paper is to extend the exponentially convex functions which are defined and exponentially convex on a cylinderical neighborhood in the Heisenberg group. They are expanded in terms of an integral transform associated to the sub-Laplacian operator. Extension of such functions on abelian Lie group are studied in [15].