Geodesic
A~Paley--Wiener theorem for generalized entire functions on infinite-dimensional spaces
Izvestiya. Mathematics , Tome 65 (2001) no. 2, pp. 403-424

Voir la notice de l'article provenant de la source Math-Net.Ru

We study entire functions on infinite-dimensional spaces. The basis is the study of spaces of Gateaux holomorphic functions that are bounded on certain subsets (bounded entire functions). The main goal is to characterize the Fourier image of the corresponding spaces of generalized entire functions (ultra-distributions) by an infinite-dimensional Paley–Wiener theorem. We introduce entire functions of exponential type and prove a generalization of the classical Paley–Wiener theorem. The crucial point of our theory is the dimension-invariant estimate given by Lemma 4.12. 
@article{IM2_2001_65_2_a6,
     author = {A. Yu. Khrennikov and H. Petersson},
     title = {A~Paley--Wiener theorem for generalized entire functions on infinite-dimensional spaces},
     journal = {Izvestiya. Mathematics },
     pages = {403--424},
     publisher = {mathdoc},
     volume = {65},
     number = {2},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2001_65_2_a6/}
}
TY  - JOUR
AU  - A. Yu. Khrennikov
AU  - H. Petersson
TI  - A~Paley--Wiener theorem for generalized entire functions on infinite-dimensional spaces
JO  - Izvestiya. Mathematics 
PY  - 2001
SP  - 403
EP  - 424
VL  - 65
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2001_65_2_a6/
LA  - en
ID  - IM2_2001_65_2_a6
ER  - 
%0 Journal Article
%A A. Yu. Khrennikov
%A H. Petersson
%T A~Paley--Wiener theorem for generalized entire functions on infinite-dimensional spaces
%J Izvestiya. Mathematics 
%D 2001
%P 403-424
%V 65
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2001_65_2_a6/
%G en
%F IM2_2001_65_2_a6
A. Yu. Khrennikov; H. Petersson. A~Paley--Wiener theorem for generalized entire functions on infinite-dimensional spaces. Izvestiya. Mathematics , Tome 65 (2001) no. 2, pp. 403-424. http://geodesic.mathdoc.fr/item/IM2_2001_65_2_a6/