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Transactions of the American Mathematical Society

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Asymptotic behavior of transforms of distributions

Author: E. O. Milton
Journal: Trans. Amer. Math. Soc. 172 (1972), 161-176
MSC: Primary 46F10; Secondary 44A10
MathSciNet review: 0310631
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Abstract: In this paper final and initial value type Abelian theorems for Laplace and Fourier transforms of certain types of distributions are obtained. The class of distributions under consideration contains the singular distributions. Thus we generalize the results previously obtained by A. H. Zemanian in two ways: we add Fourier transforms to those considered, and we also deal with a larger class of distributions.

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  • [1] E. J. Beltrami and M. R. Wohlers, Distributions and the boundary values of analytic functions, Academic Press, New York-London, 1966. MR 0208362
  • [2] Gustav Doetsch, Handbuch der Laplace-Transformation. Band I. Theorie der Laplace-Transformation, Verlag Birkhäuser, Basel, 1950 (German). MR 0043253
  • [3] Avner Friedman, Generalized functions and partial differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0165388
  • [4] Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée, Hermann, Paris, 1966 (French). MR 0209834
  • [5] E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Clarendon Press, Oxford, 1948.
  • [6] François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131
  • [7] A. H. Zemanian, Distribution theory and transform analysis. An introduction to generalized functions, with applications, McGraw-Hill Book Co., New York-Toronto-London-Sydney, 1965. MR 0177293

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Keywords: Asymptotic, distributions, Laplace transform, Fourier transform, Abelian theorems
Article copyright: © Copyright 1972 American Mathematical Society

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