Article
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Group-Frames for Banach Spaces
Version 1
: Received: 6 April 2023 / Approved: 6 April 2023 / Online: 6 April 2023 (09:59:29 CEST)
How to cite: Krishna, K.M. Group-Frames for Banach Spaces. Preprints 2023, 2023040085. https://doi.org/10.20944/preprints202304.0085.v1 Krishna, K.M. Group-Frames for Banach Spaces. Preprints 2023, 2023040085. https://doi.org/10.20944/preprints202304.0085.v1
Abstract
In the literature, frames generated by unitary representations of groups (known as group-frames) are studied only for Hilbert spaces. We make first study of frames for Banach spaces generated by isometric invertible representations of discrete groups on Banach spaces. These frames are characterized using left regular, right regular, Gram-matrices and group-matrices on classical sequence spaces. A sufficiently large collection of functional-vector pairs using the double commutant of the representation is identified which generate group-frames for Banach spaces. Subsequently, we study Schauder frames generated by time-frequency shift operators on finite dimensional Banach spaces. We derive Moyal formula, fundamental identity of Gabor analysis, Wexler-Raz criterion and Ron-Shen duality in functional form.
Keywords
Frame; group; representation
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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