Asymptotic expansions of some integral transforms by using generalized functions

Zayed, Ahmed I.

doi:10.1090/S0002-9947-1982-0662067-9

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.

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