Multivariate Gabor frames for operators in matrix-valued signal spaces over locally compact abelian groups

Jindal, D.Sinha, U.K.Verma, G.2025-12-182025-12-182021International Journal of Wavelets, Multiresolution and Information Processing, 2021; 19(2, article no. 2050069):1-240219-69131793-690Xhttps://hdl.handle.net/11541.2/146051In this paper, we study multivariate Gabor frames in matrix-valued signal spaces over locally compact abelian (LCA) groups, where the lower frame condition depends on a bounded linear operator T on the underlying matrix-valued signal space. This type of Gabor frame is also known as a multivariate T-Gabor frame. By extending work of Gavruta, we present necessary and sufficient conditions for the existence of T-Gabor frames of multivariate matrix-valued Gabor systems. Some operators which can transform multivariate matrix-valued Gabor and T-Gabor frames into T-Gabor frames in terms of adjointable operators are discussed. Finally, we give a Paley-Wiener-type perturbation result for multivariate matrix-valued T-Gabor frames.enCopyright 2020 World Scientific Publishing Companybessel sequencegabor framehilbert frameMultivariate Gabor frames for operators in matrix-valued signal spaces over locally compact abelian groupsJournal article10.1142/S02196913205006912-s2.0-85097563771