Tauberian theorems for distributional wavelet transform
Katerina Saneva, Aneta Bučkovska · Integral Transforms and Special Functions · 2007
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∈𝒮′(ℝ). Additionally, we proved that the distribution 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.