Tables of Fourier Transforms and Fourier Transforms of Distributions (Paperback)

Descripción:

Paperback. This book presents a comprehensive collection of integrals of the Fourier transformation type. It should be useful for everyone concerned with Fourier transform methods, which have found a great variety of applications in the natural sciences. This book presents a collection of integrals of the sine-, cosine- and exponential Fourier transforms of functions f(x). It is the second, considerably enlarged version of the author's previous publication "Tabellen zur Fourier Transformation" (Springer-Verlag 1957). In addition to numerous new results in Parts I-III, a new Part IV has been introduced dealing with problems in mathematical statistics. The aim of the book is to serve as a reference work for all those whose main interest is in the application of Fourier transform methods. These methods have found a wide variety of applications in the natural and technical sciences. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de ref. del artículo 9783540506300

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Sinopsis:

Reseña del editor: 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.