On the Laplace transform of a temperate distribution supported by a cone
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- by Bent E. Petersen PDF
- Proc. Amer. Math. Soc. 35 (1972), 123-128 Request permission
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
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W. F. Donoghuc, Jr., Distributions and Fourier transforms, Academic Press, New York, 1969.
- Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, IX-X, Hermann, Paris, 1966 (French). Nouvelle édition, entiérement corrigée, refondue et augmentée. MR 0209834
- K. T. Smith, Formulas to represent functions by their derivatives, Math. Ann. 188 (1970), 53–77. MR 282046, DOI 10.1007/BF01435415
- R. F. Streater and A. S. Wightman, PCT, spin and statistics, and all that, W. A. Benjamin, Inc., New York-Amsterdam, 1964. MR 0161603
Additional Information
- © Copyright 1972 American Mathematical Society
- 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