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Distributional Fourier Transform and Convolution Associated to Chébli-Trimèche Hypergroups

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Abstract.

 In this paper we investigate the convolution and the generalized Fourier transform related to Chébli-Trimèche hypergroups on new spaces of distributions. Boundedness, smoothness, uniqueness, and inversion theorems are established for this transform, as well as the main properties of the convolution. The theory developed is used in solving a differential equation involving a singular differential operator.

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Authors and Affiliations

  1. Universidad de La Laguna, Tenerife, Spain, , , , , , ES

    J. J. Betancor, J. D. Betancor & J. M. Méndez

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  1. J. J. Betancor
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  2. J. D. Betancor
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  3. J. M. Méndez
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(Received 26 January 2000; in final form 24 July 2001)

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Betancor, J., Betancor, J. & Méndez, J. Distributional Fourier Transform and Convolution Associated to Chébli-Trimèche Hypergroups. Mh Math 134, 265–286 (2002). https://doi.org/10.1007/s605-002-8262-x

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  • DOI: https://doi.org/10.1007/s605-002-8262-x

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