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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Asymptotic expansions of some integral transforms by using generalized functions
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by Ahmed I. Zayed PDF
Trans. Amer. Math. Soc. 272 (1982), 785-802 Request permission

Abstract:

The technique devised by Wong to derive the asymptotic expansions of multiple Fourier transforms by using the theory of Schwartz distributions is extended to a large class of integral transforms. The extension requires establishing a general procedure to extend these integral transforms to generalized functions. Wong’s technique is then applied to some of these integral transforms to obtain their asymptotic expansions. This class of integral transforms encompasses, among others, the Laplace, the Airy, the $K$ and the Hankel transforms.
References
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 272 (1982), 785-802
  • MSC: Primary 41A60; Secondary 44A05, 46F12
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0662067-9
  • MathSciNet review: 662067