Tempered Distributions and the Fourier Transform

Ram P. Kanwal
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Ram P. Kanwal: The Pennsylvania State University, Department of Mathematics

Chapter Chapter 6 in Generalized Functions, 2004, pp 139-177 from Springer

Abstract: Abstract In attempting to define the Fourier transform of a distribution t (x), we would like to use the formula (in R 1) 1 $$ \hat t\left( u \right) = F\left( {t\left( x \right)} \right) = \int_{ - \infty }^\infty {e^{iux} t\left( x \right)dx.} $$ .

Keywords: Fourier Transform; Temper Distribution; Inverse Fourier Transform; Summation Formula; Hermite Function (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-8176-8174-6_6

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