Continuous Wavelet Transform of Schwartz Tempered Distributions in S0(Rn)

Abstract

In this paper, we define a continuous wavelet transform of a Schwartz tempered distribution f 2 S0 (Rn) with wavelet kernel y 2 S(Rn) and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of S0 (Rn). It turns out that the wavelet transform of a constant distribution is zero and our wavelet inversion formula is not true for constant distribution, but it is true for a non-constant distribution which is not equal to the sum of a non-constant distribution with a non-zero constant distribution.