On the space of periodic distributions with multi-dimensional wavelet packet transform

The multi-dimensional wavelet packet transform on the space of infinitely differentiable 2π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\pi$$\end{document} periodic functions is defined and extended to periodic distributions by giving justification to its continuity. Properties of the extended transform under weak* topology are discussed.