Tauberian theorems for distributional wavelet transform.

In this paper we investigated the asymptotic behaviour at 0 and infinity of the distributional wavelet transform. Assuming that the wavelet transform Wg 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∈S'(). Additionally, we proved that the distribution [image omitted] has the S-asymptotics at infinity equal to zero if its wavelet transform Wg f(b, a) has the S-asymptotics at infinity with respect to the variable b. [ABSTRACT FROM AUTHOR]