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On the Laplace transform of a temperate distribution supported by a cone

Author: Bent E. Petersen
Journal: Proc. Amer. Math. Soc. 35 (1972), 123-128
MSC: Primary 46F10
MathSciNet review: 0298414
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Abstract: The temperate distributions supported by a closed convex salient cone are characterized by explicit polynomial growth of the Laplace transform at infinity and at the boundary of the cylinder over the dual cone. This result is then used to characterize by their Laplace transforms the smooth kernels of degree $ \lambda - n$ where $ \lambda $ is positive.

References [Enhancements On Off] (What's this?)

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  • [2] Laurent Schwartz, Théorie des distributions, Publ. Inst. Math. Univ. Strasbourg, no. 9-10, Nouvelle édition, entièrement corrigee, refondue et augmentée, Hermann, Paris, 1966. MR 35 #730. MR 0209834 (35:730)
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Keywords: Laplace transform, temperate distribution
Article copyright: © Copyright 1972 American Mathematical Society

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