Asymptotic expansion of distributional wavelet transform
Katerina Saneva, Aneta Bučkovska · Integral Transforms and Special Functions · 2006
In this paper, a quasiasymptotic behaviour and a quasiasymptotic expansion at , x 0>0 of a distribution from are defined and applied to the distributional wavelet transform. By assuming that the distribution f∈𝒮′ b + (ℝ) has a quasiasymptotic at b +, b>0, we determined the ordinary asymptotic behaviour at 0+ of its wavelet transform 𝒲 g f(b, a) with respect to the variable a. We also analysed the asymptotic expansion at 0+ of the wavelet transform with respect to both variables a and b (with respect to the variable a) of distributions from 𝒮′+(ℝ) (𝒮′ b + (ℝ)) with appropriate quasiasymptotic expansion at 0+ (b +).