MULTIDIMENSIONAL TAUBERIAN THEOREMS FOR VECTOR-VALUED DISTRIBUTIONS

被引：14
|
作者：
Pilipovic, Stevan [1 ]
Vindas, Jasson [2 ]
机构：
[1] Univ Novi Sad, Dept Math & Informat, Novi Sad 21000, Serbia
[2] Univ Ghent, Dept Math, B-9000 Ghent, Belgium
来源：
PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD | 2014年 / 95卷 / 109期
关键词：
Abelian and Tauberian theorems; vector-valued distributions; quasiasymptotics; slowly varying functions; Laplace transform; wavelet transform; regularizing transforms; asymptotic behavior of generalized functions; PRIME NUMBER THEOREM; GENERALIZED-FUNCTIONS; TEMPERED DISTRIBUTIONS; FOURIER-SERIES; CONVERGENCE; BEHAVIOR; ORIGIN;
D O I：
10.2298/PIM1409001P
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove several Tauberian theorems for regularizing transforms of vector-valued distributions. The regularizing transform of f is given by the integral transform M-phi(f)(x, y) = (f * phi(y))(x), (x, y) is an element of R-n x R+, with kernel phi(y) (t) = y(-n)phi(t/y). We apply our results to the analysis of asymptotic stability for a class of Cauchy problems, Tauberian theorems for the Laplace transform, the comparison of quasiasymptotics in distribution spaces, and we give a necessary and sufficient condition for the existence of the trace of a distribution on {x(0)} x R-m. In addition, we present a new proof of Littlewood's Tauberian theorem.
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页码：1 / 28
页数：28
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