Multidimensional Tauberian theorems for generalized functions. (English) Zbl 1373.46032

Drozhzhinov, Yu. N.

Russ. Math. Surv. 71, No. 6, 1081-1134 (2016); translation from Usp. Mat. Nauk 71, No. 6, 90-154 (2016).

Summary: This is a brief survey of multidimensional Tauberian theorems for generalized functions. Included are theorems of Hardy-Littlewood type, Tauberian and abelian comparison theorems of Keldysh type, theorems of Wiener type, and Tauberian theorems for generalized functions with values in Banach spaces.

MSC:

46F12	Integral transforms in distribution spaces
40E05	Tauberian theorems
40-02	Research exposition (monographs, survey articles) pertaining to sequences, series, summability

Keywords:

generalized functions; quasi-asymptotics; abelian theorems; Tauberian theorems; quasi-asymptotic boundedness; regularly varying functions; automodel functionals