Geodesic
Remarques sur la formule sommatoire de Poisson
Studia Mathematica, Tome 109 (1994) no. 3, pp. 303-316

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-109-3-303-316

Jean Pierre Kahane 1

1 
@article{10_4064_sm_109_3_303_316,
     author = {Jean Pierre Kahane},
     title = {Remarques sur la formule sommatoire de {Poisson}},
     journal = {Studia Mathematica},
     pages = {303--316},
     publisher = {mathdoc},
     volume = {109},
     number = {3},
     year = {1994},
     doi = {10.4064/sm-109-3-303-316},
     language = {fr},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-109-3-303-316/}
}
TY  - JOUR
AU  - Jean Pierre Kahane
TI  - Remarques sur la formule sommatoire de Poisson
JO  - Studia Mathematica
PY  - 1994
SP  - 303
EP  - 316
VL  - 109
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-109-3-303-316/
DO  - 10.4064/sm-109-3-303-316
LA  - fr
ID  - 10_4064_sm_109_3_303_316
ER  - 
%0 Journal Article
%A Jean Pierre Kahane
%T Remarques sur la formule sommatoire de Poisson
%J Studia Mathematica
%D 1994
%P 303-316
%V 109
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-109-3-303-316/
%R 10.4064/sm-109-3-303-316
%G fr
%F 10_4064_sm_109_3_303_316
Jean Pierre Kahane. Remarques sur la formule sommatoire de Poisson. Studia Mathematica, Tome 109 (1994) no. 3, pp. 303-316. doi: 10.4064/sm-109-3-303-316

Cité par Sources :