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Tables of Fourier Transforms and Fourier Transforms of Distributions (Paperback, Softcover reprint of the original 1st ed. 1990)
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Tables of Fourier Transforms and Fourier Transforms of Distributions (Paperback, Softcover reprint of the original 1st ed. 1990)
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These tables represent a new, revised and enlarged version of the
previously published book by this author, entitled "Tabellen zur
Fourier Transformation" (Springer Verlag 1957). Known errors have
been correc- ted, apart from the addition of a considerable number
of new results, which involve almost exclusively higher functions.
Again, the follow- ing tables contain a collection of integrals of
the form J f(x)cos(xy)dx Fourier Cosine Transform (Al o (B) J
f(x)sin(xy)dx Fourier Sine Transform o (C) ge(y) = J f(x)eixYdx
Exponential Fourier Transform -00 Clearly, (A) and (B) are special
cases of (C) if f(x) is respec- tively an even or an odd function.
The transform parameter y in (A) and (B) is assumed to be positive,
while in (C) negative values are also included. A possible analytic
continuation to complex parameters y* should present no
difficulties. In some cases the result function g(y) is given over
a partial range of y only. This means that g(y) for the remaining
part of y cannot be given in a reasonably simple form. Under
certain conditions the following inversion formulas for (A), (B),
(C) hold: (A' ) f(x) = 2 J g (y)cos(xy)dy 11 0 c 2 J (B') f (x)
gs(y)sin(xy)dy 11 0 -1 00 -ix (C' ) f(x) = (211) J ge(y)e Ydy In
the following parts I, II, III tables for the transforms (A), (B)
and (C) are given.
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