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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Asymptotic behavior of transforms of distributions
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by E. O. Milton PDF
Trans. Amer. Math. Soc. 172 (1972), 161-176 Request permission

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.
References
  • E. J. Beltrami and M. R. Wohlers, Distributions and the boundary values of analytic functions, Academic Press, New York-London, 1966. MR 0208362
  • Gustav Doetsch, Handbuch der Laplace-Transformation. Band I. Theorie der Laplace-Transformation, Verlag Birkhäuser, Basel, 1950 (German). MR 0043253
  • Avner Friedman, Generalized functions and partial differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0165388
  • 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
  • E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Clarendon Press, Oxford, 1948.
  • François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131
  • 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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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 172 (1972), 161-176
  • MSC: Primary 46F10; Secondary 44A10
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0310631-2
  • MathSciNet review: 0310631