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Domains of holomorphy for Fourier transforms of solutions to discrete convolution equations

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Abstract

We study solutions to convolution equations for functions with discrete support in ℝn, a special case being functions with support in the integer points. The Fourier transform of a solution can be extended to a holomorphic function in some domains in ℂn, and we determine possible domains in terms of the properties of the convolution operator.

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Authors and Affiliations

  1. Department of Information Technology, Uppsala University, Uppsala, SE-751 05, Sweden

    Christer O. Kiselman

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  1. Christer O. Kiselman
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Correspondence to Christer O. Kiselman.

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In memory of Professor LU QiKeng (1927–2015)

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Kiselman, C.O. Domains of holomorphy for Fourier transforms of solutions to discrete convolution equations. Sci. China Math. 60, 1005–1018 (2017). https://doi.org/10.1007/s11425-015-9029-0

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  • DOI: https://doi.org/10.1007/s11425-015-9029-0

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