Geodesic
A Wiener-type Tauberian theorem for generalized functions of slow growth
Sbornik. Mathematics, Tome 189 (1998) no. 7, pp. 1047-1086 
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/
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     author = {Yu. N. Drozhzhinov and B. I. Zavialov},
     title = {A {Wiener-type} {Tauberian} theorem for generalized functions of slow growth},
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     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_7_a4/}
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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.

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