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Fourier Analysis and Applications pp 283–296Cite as

The Fourier Transform of Distributions

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Part of the book series: Texts in Applied Mathematics ((TAM,volume 30))

Abstract

We are going to extend the Fourier transform to distributions by interpreting the transpose formula we obtained for functions. Consider the following formal computation. Let f be a function in L 1(ℝ) and let φ be in D.

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Authors and Affiliations

  1. Université Joseph Fourier (Grenoble I), France

    Claude Gasquet

  2. Laboratoire LMCIMAG, Tour IRMA, BP 53, 38041, Grenoble, Cedex 09, France

    Patrick Witomski (Directeur)

Authors
  1. Claude Gasquet
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  2. Patrick Witomski
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© 1999 Springer Science+Business Media New York

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Gasquet, C., Witomski, P. (1999). The Fourier Transform of Distributions. In: Fourier Analysis and Applications. Texts in Applied Mathematics, vol 30. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1598-1_31

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  • DOI: https://doi.org/10.1007/978-1-4612-1598-1_31

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7211-3

  • Online ISBN: 978-1-4612-1598-1

  • eBook Packages: Springer Book Archive

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