The integral wavelet transform of convolutors

Wavelet transforms in generalized Fock spaces

“…In particular how to apply them to singtdar distributions or non-regular distributions such as the Dirac delta functional which again in the authors opinion is a very "rough" object. Several research papers regarding the implementation of wavelets to distributions can be found in the research done by Walter [14][15][16][17][18][19][20] and Mikusinski and Mort [9]. We will extend several of these results.…”

“…Also the inversion of the wavelet transform stemming from the admissibility condition can also be found within these references. We will begin our analysis by considering the wavelet transform as a special type of convolution as in Mallat [21][22][23][24] and Milusinski and Mott [9]. This inequality will remain valid for any mother wavelet, Ca, r(t), which has been normalized in the L2(q) norm.…”

“…The application of wavelets to image processing has been developed as a convolution operator in the work of Mallat [21][22][23][24] and further developed in a mathematical milieu in the work of Mikusinski and Mort [9].…”