A family of operators satisfying a Poisson-type summation formula, and a characterization of the Fourier transform

Mon, 30/04/2012 - 14:00
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We study to which extent the Poisson summation formula determines the Fourier transform. The answer is positive under certain technical smoothness and rate of decay conditions. This study leads to a class of unitary operators on L^2 that satisfy a weighted form of the Poisson summation formula, which we explicitly diagonalize, with eigenvalues related to associated L-functions.