The Watson Fourier transform on a certain class of generalized functions

In this paper, we first build an appropriate Boehmian space on which a classical theory of the Watson Fourier transform is extended. We provide convolution products, convolution theorems and generate their associated spaces of Boehmian. The properties of the extended Watson Fourier transform are also established. Moreover, continuity with respect to δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta$$\end{document} and Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta$$\end{document}-convergence is discussed.