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International Journal of Mathematics and Mathematical Sciences
Volume 21, Issue 4, Pages 643-652

Homogeneous cones and abelian theorems

1Département de Mathématiques, Université de Montpellier III, France
2Mathematical Institute, Belgrade, Serbia

Received 31 October 1996; Revised 26 September 1997

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with analysis on homogeneous cones in n. This subject has its origins in one-dimensional topics that are connected, often implicitely, with some group properties. The homogeneous cones are open convex cones in n that are at the same time homogeneous spaces, and they are more general than the classical, or symmetric cones. As an example of application of the theory of homogeneous cones we study the asymptotic behaviour of some integral transforms.