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In this paper, we study Gabor frames in the matrix-valued signal space [Formula: see text], where [Formula: see text] is a locally compact abelian group which is metrizable and [Formula: see text]-compact, and [Formula: see text] is a positive integer. First, we give sufficient conditions on scalars in an infinite combination of vectors (from a giv...
G\v avruta studied atomic systems in terms of frames for range of operators (that is, for subspaces), namely $K$-frames, where the lower frame condition is controlled by the Hilbert-adjoint of a bounded linear operator $K$. For a locally compact abelian group G and a positive integer $n$, we study frames of matrix-valued Gabor systems in the matrix...
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 [Formula: see text] on the underlying matrix-valued signal space. This type of Gabor frame is also known as a multivariate [Formula: see text]-Gabor frame. B...
