Remarques sur la formule sommatoire de Poisson
Volume 109 / 1994
Studia Mathematica 109 (1994), 303-316
DOI: 10.4064/sm-109-3-303-316
Abstract
It is well known that the condition "f ∈ L¹ and f̂ ∈ L¹" is not sufficient to ensure the validity of the Poisson summation formula ∑f(k) = ∑f̂(k). We discuss here a stronger condition "$x^a f ∈ L^p$ and $ξ^b f̂ ∈ L^q$" and see for which values of a and b the condition is sufficient.
