Subspace mixed rational time-frequency multiwindow Gabor frames and their Gabor duals

For a usual multiwindow Gabor system, all windows share common time-frequency shifts. A mixed multiwindow Gabor system is one of its generalizations, for which time-frequency shifts vary with the windows. This paper addresses subspace mixed multiwindow Gabor systems with rational time-frequency product lattices. It is a continuation of (Li and Zhang in Abstr. Appl. Anal. 2013:357242, 2013; Zhang and Li in J. Korean Math. Soc. 51:897–918, 2014). In (Li and Zhang in Abstr. Appl. Anal. 2013:357242, 2013) we dealt with discrete subspace mixed Gabor systems and in (Zhang and Li in J. Korean Math. Soc. 51:897–918, 2014) with L2(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L^{2}(\mathbb{R})$\end{document} ones. In this paper, using a suitable Zak transform matrix method, we characterize subspace mixed multiwindow Gabor frames and their Gabor duals, obtain explicit expressions of Gabor duals, and characterize the uniqueness of Gabor duals. We also provide some examples, which show that there exist significant differences between mixed multiwindow Gabor frames and usual multiwindow Gabor frames.