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Characterization of the support for the hypergeometric Fourier transform of the W-invariant functions and distributions on R-d and Roe's theorem
Journal article   Open access  Peer reviewed

Characterization of the support for the hypergeometric Fourier transform of the W-invariant functions and distributions on R-d and Roe's theorem

Hatem Mejjaoli and Khalifa Trimeche
Journal of inequalities and applications, Vol.2014(1)
26/02/2014
DOI: https://doi.org/10.1186/1029-242X-2014-99

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
In this paper, we establish real Paley-Wiener theorems for the hypergeometric Fourier transform on R-d. More precisely, we characterize the functions of the generalized Schwartz space S-2(R-d)(W) and of L-Ak(p) (R-d)(W), 1 <= p <= 2, whose hypergeometric Fourier transform has bounded, unbounded, convex, and nonconvex support. Finally we study the spectral problem on the generalized tempered distributions S'(2) (R-d)(W).
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https://doi.org/10.1186/1029-242X-2014-99View
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