Abstract

The aim of this paper is to analyze the asymptotic behavior at infinity of the integral wavelet transform of somewhat more general elements than $L^2$ functions, namely generalized functions from the space of exponential distributions ${\Cal K}_1'$. We prove both an Abelian and a Tauberian type theorem at infinity for the integral wavelet transform.

Keywords: Integral wavelet transform, generalized functions, Abelian type theorems, Tauberian type theorems.

MSC: 42C05

Pages:  215--220     

Volume  49 ,  Issue  3$-$4 ,  1997