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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Asymptotic expansions of some integral transforms by using generalized functions


Author: Ahmed I. Zayed
Journal: Trans. Amer. Math. Soc. 272 (1982), 785-802
MSC: Primary 41A60; Secondary 44A05, 46F12
MathSciNet review: 662067
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0662067-9
PII: S 0002-9947(1982)0662067-9
Keywords: Asymptotic expansion, generalized function, integral transform
Article copyright: © Copyright 1982 American Mathematical Society