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Fourier analysis on Colombeau’s algebra of generalized functions

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Abstract

In this paper we study Fourier transforms on Colombeau’s algebra. We present a Paley-Wiener theorem for generalized functions and introduce generalized functions with compact spectrum. When restricted to distributions this notion coincides with the classical notion of distributions of compact spectrum. We also define subalgebras where the Fourier transform is well behaved in the classical algebraic sense.

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Authors and Affiliations

  1. Departamento de Matemática Pura, Universidade Federal do Rio de Janeiro, Caixa Postal 68.530, 21910, Rio de Janerio, Brazil

    Roberto Luiz Soraggi

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  1. Roberto Luiz Soraggi
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Soraggi, R.L. Fourier analysis on Colombeau’s algebra of generalized functions. J. Anal. Math. 69, 201–227 (1996). https://doi.org/10.1007/BF02787107

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  • DOI: https://doi.org/10.1007/BF02787107

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