Multivariate Gabor frames for operators in matrix-valued signal spaces over locally compact abelian groups
Date
2021
Authors
Jindal, D.
Sinha, U.K.
Verma, G.
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International Journal of Wavelets, Multiresolution and Information Processing, 2021; 19(2, article no. 2050069):1-24
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Abstract
In 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.
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Copyright 2020 World Scientific Publishing Company