Fourier Transforms of Distributions and Their Inverses

Released on by Fritz Oberhettinger
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  • Fourier Transforms of Distributions and Their Inverses Book Detail

  • Author : Fritz Oberhettinger
  • Release Date : 2014-07-03
  • Publisher : Academic Press
  • Genre : Mathematics
  • Pages : 180
  • ISBN 13 : 148321902X
  • File Size : 37,37 MB
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Fourier Transforms of Distributions and Their Inverses by Fritz Oberhettinger PDF Summary

Book Description: Fourier Transforms of Distributions and Their Inverses: A Collection of Tables is a collection of tables on the integrals of Fourier transforms of distributions and their inverses involving the class of functions which are nonnegative and integrable over the interval. The emphasis is on the probability densities, and a number of examples are provided. This book is organized into two parts and begins with an introduction to those properties of characteristic functions which are important in probability theory, followed by a description of the tables and their use. The first three tables contain Fourier transforms of absolutely continuous distribution functions, namely, even functions (including Legendre functions); functions vanishing identically for negative values of the argument (including arbitrary powers); and functions that do not belong to either of the above classes. The transform pairs are numbered consecutively and arranged systematically according to the analytical character of the frequency function. The next two tables give the inverse transforms of the functions listed in the first and third tables, respectively. This monograph will appeal to students and specialists in the fields of probability and mathematical statistics.

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Distribution Theory and Transform Analysis

Distribution Theory and Transform Analysis

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Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote t