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A generalized Fourier inversion Theorem

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Abstract

In this work we define operator-valued Fourier transforms for suitable integrable elements with respect to the Plancherel weight of a (not necessarily Abelian) locally compact group. Our main result is a generalized version of the Fourier inversion Theorem for strictly-unconditionally integrable Fourier transforms. Our results generalize and improve those previously obtained by Ruy Exel in the case of Abelian groups.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, SC, Brazil

    Alcides Buss

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  1. Alcides Buss
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Correspondence to Alcides Buss.

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Supported by CAPES, Brazil.

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Buss, A. A generalized Fourier inversion Theorem. Bull Braz Math Soc, New Series 39, 555–571 (2008). https://doi.org/10.1007/s00574-008-0004-6

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  • DOI: https://doi.org/10.1007/s00574-008-0004-6

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