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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-1972-0298414-9
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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0298414-9
Keywords: Laplace transform, temperate distribution
Article copyright: © Copyright 1972 American Mathematical Society