Asymptotic behaviour of wavelet coefficients
Katerina Saneva · Integral Transforms and Special Functions · 2009
In this article, we investigate the asymptotic behaviour at infinity of the wavelet coefficients. Assuming that the distribution f∈𝒮′(ℝ) has the quasiaymptotics at 0 (respectively, the S-asymptotics at infinity) related to a regularly varying function, we obtain results for the asymptotic behaviour at infinity of its wavelet coefficients. Additionally, we analyse the boundedness of the wavelet coefficients of the quasiasymptotically bounded distribution.