On WH Packets in $L^2(\mathbb{R})$ - Kaushik, S. K.; Singh, Ghanshyam; Virender, . (Communications in Mathematics and Applications, 2012)
WH packets with respect to a Gabor system (frame) have been introduced and it has been shown with the help of examples that WH packets with respect to a Gabor frame may not be a frame for $L^2(\mathbb{R})$. A sufficient condition under which WH packets with respect to a Gabor frame is a frame for $L^2(\mathbb{R})$ has been given. A necessary and sufficient condition has also been given in this direction. Further, finite sum of Gabor frames has been considered and sufficient conditions under which finite sum of Gabor frames is a frame for $L^2(\mathbb{R})$ have been given. Finally, stability of Gabor frames has been studied and sufficient conditions in this direction have been obtained.
Keywords: WH packets