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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].
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.
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.
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.
The Transition in Social Housing in Germany – New Challenges and New Players After 60 Years
Ralf Zabel,권영상 대한건축학회 2019 Architectural research Vol.21 No.1
Social housing has a long history in Germany from the first still existing social housing ever, the “Fuggerei” in Augsburg (founded in 1521), over the last 100 years from the end of World War I to today’s situation where the need in social housing has increased while the number of housing projects and the number of existing apartments in this program has decreased or ended. Socio-economic changes like demographic evolution, more single households, greater working abilities in bigger cities and an unforeseen highly increased number of migrants within Europe mostly but also from other countries led to the need of affordable housing for a growing number of people who are not able to care for their housing needs in their own responsibility. This is especially true for bigger cities, where the offer of affordable housing is nearly non-existing any more. The family Fugger, a trade and banking dynasty at their time, established a very modern housing concept, providing good and healthy living space for their workers. In 2018 now some trade companies, discounters (ALDI, LIDL, Norma) and IKEA announce to combine their interest in sales in the inner cities with the municipal interest of redensification of existing housing areas and conversion to ecological urban reconstructuring.
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.