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Poisson summation formula in weighted Lebesgue spaces (2412.07661v1)

Published 10 Dec 2024 in math.CA

Abstract: We characterize the parameters $(\alpha,\beta,p,q)$ for which the condition $f|x|^\alpha\in L^p$ and $\widehat{f}|\xi|^\beta\in L^q$ implies the validity of the Poisson summation formula, thus completing the study of Kahane and Lemari\'e-Rieusset.