Geodesic
A Wiener-type Tauberian theorem for generalized functions of slow growth
Sbornik. Mathematics, Tome 189 (1998) no. 7, pp. 1047-1086

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

The paper is devoted to the extension of Wiener-type Tauberian theorems to the case of generalized functions of slow growth. A functional is shown to have asymptotics (in the weak sense) if and only if it has asymptotics on a 'test' function whose Mellin transform is bounded away from zero in a certain strip of the complex plane related to the order of the functional in question. Applications of this result are also considered; in particular, several theorems on the lack of compensation of the singularities of holomorphic functions are proved. 
@article{SM_1998_189_7_a4,
     author = {Yu. N. Drozhzhinov and B. I. Zavialov},
     title = {A {Wiener-type} {Tauberian} theorem for generalized functions of slow growth},
     journal = {Sbornik. Mathematics},
     pages = {1047--1086},
     publisher = {mathdoc},
     volume = {189},
     number = {7},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_7_a4/}
}
TY  - JOUR
AU  - Yu. N. Drozhzhinov
AU  - B. I. Zavialov
TI  - A Wiener-type Tauberian theorem for generalized functions of slow growth
JO  - Sbornik. Mathematics
PY  - 1998
SP  - 1047
EP  - 1086
VL  - 189
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1998_189_7_a4/
LA  - en
ID  - SM_1998_189_7_a4
ER  - 
%0 Journal Article
%A Yu. N. Drozhzhinov
%A B. I. Zavialov
%T A Wiener-type Tauberian theorem for generalized functions of slow growth
%J Sbornik. Mathematics
%D 1998
%P 1047-1086
%V 189
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1998_189_7_a4/
%G en
%F SM_1998_189_7_a4
Yu. N. Drozhzhinov; B. I. Zavialov. A Wiener-type Tauberian theorem for generalized functions of slow growth. Sbornik. Mathematics, Tome 189 (1998) no. 7, pp. 1047-1086. http://geodesic.mathdoc.fr/item/SM_1998_189_7_a4/