Abstract
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.
Acknowledgements
The authors are grateful to Professor Stevan Pilipović from University of Novi Sad for his guidance and comments during the preparation of this paper.