Holomorphic extension of certain discrete functions on ℤ n and the related problems

Ahmed Abouelaz () and Radouan Daher ()
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Ahmed Abouelaz: University Hassan II of Casablanca, Faculty of Sciences Aïn Chock
Radouan Daher: University Hassan II of Casablanca, Faculty of Sciences Aïn Chock

Indian Journal of Pure and Applied Mathematics, 2015, vol. 46, issue 1, 25-40

Abstract: Abstract In this paper, we construct an holomorphic extension of certain functions on ℤ n . We deduce a discrete Gutzmer’s formula for the discrete Fourier transform (see Theorem 4.4). In addition, we prove the Hardy-Littlewood inequality for the classical Radon transform on ℝ n (see Theorem 4.7). In this work, we use the techniques of the diophantine integral geometry and the estimate method in certain weighted L 2-spaces.

Keywords: Discrete fourier transform; discrete Gutzmer’s formula; Radon transform; Hardy-Littlewood inequality (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s13226-015-0105-z

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