JP Journal of Algebra, Number Theory and Applications
Volume 12, Issue 2, Pages 205 - 229
(December 2008)
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A TRANSFORMATION OF HANKEL TYPE ON THE FIELD OF p-ADIC NUMBERS
Xian-Jin Li (USA)
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Abstract: In
this paper a Hankel type transformation is found on the field of p-
adic numbers, for which we have the inversion formula and the Plancherel
formula. This transformation is defined by a new Bessel type function which has
remarkable properties, and is an analogue of the classical Hankel transformation
[4]. A relation between the Hankel type transformation and the Fourier
transformation is obtained. A formula is given for the Hankel type transform of
a general function. |
Keywords and phrases: Bessel function, Fourier transform, inversion formula, Plancherel formula. |
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