Tauberian theorems for distributional wavelet transform

被引：3

作者：

Saneva, Katerina ^{[1
]}

Buckovska, Aneta ^{[1
]}

机构：

[1] Univ Ss Cyril & Methodius, Fac Elect Engn, Dept Math & Phys, Skopje 1000, Macedonia

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2007年 / 18卷 / 05期

关键词：

wavelet transform; quasiasymptotic behaviour; S-asymptotics;

D O I：

10.1080/10652460701318095

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigated the asymptotic behaviour at 0 and infinity of the distributional wavelet transform. Assuming that the wavelet transform W(g)f (b, a) has the ordinary asymptotic behaviour at 0 (resp. at infinity) with respect to both variables ( resp. to the variable b), we obtained the result for the quasiasymptotic behaviour (resp. the S-asymptotics) at 0 ( resp. at infinity) of the distribution f is an element of S'(R). Additionally, we proved that the distribution f is an element of D'(L2) (R) has the S-asymptotics at infinity equal to zero if its wavelet transform W(g)f ( b, a) has the S-asymptotics at infinity with respect to the variable b.

引用

页码：359 / 368

页数：10