We study matrix-valued Gabor Bessel sequences and frames in the matrix-valued space $L^2(G, \mathbb{C}^{n\times n})$, where $G$ is a locally compact abelian group and $n$ is a positive integer. Firstly, we show that the Bessel condition (or upper frame condition) can be extended from $L^2(G)$ to its associated matrix-valued signal space $L^2(G,\mathbb{C}^{n\times n})$, and conversely. However, this is not true for the lower frame condition. Secondly, we give sufficient conditions for the extension of a pair of matrix-valued Bessel sequences to matrix-valued dual frames over LCA groups. A special class of matrix-valued dual generators is given. It is shown that the symmetric windows associated with a given matrix-valued Gabor frames constitutes a Gabor frame in matrix-valued spaces over LCA groups.
Vashisht, L., & Sinha, U. (2023). On matrix-valued Gabor Bessel sequences and dual frames over locally compact abelian groups. Khayyam Journal of Mathematics, 9(1), 89-101. https://doi.org/10.22034/kjm.2022.354990.2625
MLA
Vashisht, L., & Sinha, U. "On matrix-valued Gabor Bessel sequences and dual frames over locally compact abelian groups", Khayyam Journal of Mathematics, 9, 1, 2023, 89-101. doi: 10.22034/kjm.2022.354990.2625
HARVARD
Vashisht L., Sinha U. (2023). 'On matrix-valued Gabor Bessel sequences and dual frames over locally compact abelian groups', Khayyam Journal of Mathematics, 9(1), pp. 89-101. doi: 10.22034/kjm.2022.354990.2625
CHICAGO
L. Vashisht & U. Sinha, "On matrix-valued Gabor Bessel sequences and dual frames over locally compact abelian groups," Khayyam Journal of Mathematics, 9 1 (2023): 89-101, doi: 10.22034/kjm.2022.354990.2625
VANCOUVER
Vashisht L., Sinha U. On matrix-valued Gabor Bessel sequences and dual frames over locally compact abelian groups. Khayyam J. Math. 2023;9(1):89-101. doi: 10.22034/kjm.2022.354990.2625
