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We characterize a class O⌸ q of nondecreasing slowly varying functions with the

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ABSTRACT. This paper deals with analysis on homogeneous cones in JR". 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 ]Rn that ar 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.