Wavelet transform of Beurling–Björck type ultradistributions

Abstract

Wavelet transform of a distribution in ${\mathcal{M}}_{\omega }^{{}^{\prime }}$ involving wavelet of infraexponential decay (subexponential decay) is studied. An inversion formula is obtained which is valid in the weak topology of ${\mathcal{D}}^{{}^{\prime }}$. A discussion on extension of the results to ultradistribution space of compact support is also given.