Abstract
Motivated by the ordinary Gabor frames in L2(ℝd) and operator-valued frames on abstract Hilbert spaces, we investigate operator-valued Gabor frames associated with locally compact Abelian groups. Necessary and sufficient conditions for an operator-valued Gabor frame to admit a Parseval/tight Gabor dual are given. In particular, we consider a special case, which includes the case of ordinary Gabor frames.
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Acknowledgments
The authors would like to thank the referee for the very thorough reading and many helpful comments and suggestions that improved the presentation of the paper.
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Russian Text © The Author(s), 2019, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2019, No. 6, pp. 66–80.
This work is supported by National Natural Science Foundation of China (No. 11671201).
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Hu, Y., Li, P. Gabor Duals for Operator-valued Gabor Frames on Locally Compact Abelian Groups. J. Contemp. Mathemat. Anal. 54, 328–338 (2019). https://doi.org/10.3103/S1068362319060025
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DOI: https://doi.org/10.3103/S1068362319060025