| Tables of Fourier Transforms and Fourier Transforms of Distributions Softcover Repri Edition Contributor(s): Oberhettinger, Fritz (Author) |
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ISBN: 3540506306 ISBN-13: 9783540506300 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: April 1990 |
| Additional Information |
| BISAC Categories: - Mathematics | Calculus - Mathematics | Group Theory - Mathematics | Functional Analysis |
| Dewey: 515.723 |
| Physical Information: 0.57" H x 6.14" W x 9.21" (0.85 lbs) 259 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |