Continuous wavelet transform of Schwartz tempered distributions

The continuous wavelet transform of Schwartz tempered distributions is investigated and derive the corresponding wavelet inversion formula (valid modulo a constant-tempered distribution) interpreting convergence in S'(\ R). But uniqueness theorem for the present wavelet inversion formula is valid for the space S'F(\ R) obtained by filtering (deleting) (i) all non-zero constant distributions from the space S'(\ R), (ii) all non-zero constants that appear with a distribution as a union. As an example, in considering the distribution x² \ 1 + x² = 1 - 1 \ 1 + x² we would omit 1 and retain only - 1 \ 1 + x². The wavelet kernel under consideration for determining the wavelet transform are those wavelets whose all the moments are non-zero. As an example, (1 + kx - 2x²)e^ - x² is such a wavelet. k is an arbitrary constant. There exist many other classes of such wavelets. In our analysis, we do not use a wavelet kernel having any of its moments zero.