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

Mon, 30/04/2012 - 14:00

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.