On a Family of Fourier Transforms
نویسنده
چکیده
A procedure leading to specific properties of the symmetric stable distribution functions results by subjecting certain generalizations of the Bessel functions Ja{t) to a limit process. 1 There arises the question as to the existence of the corresponding distributions in case the limit process involved is omitted. The object of this note is to delimit the conditions under which the answer is affirmative. It turns out that the situation is quite different from that resulting in the limiting case of stability. Let L(t; ) denote the Fourier transform,
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