Frames and system of translates of Hilbert C⁎-module valued functions

In this paper, we investigate three types of problems dealing with frames in L2(Rn,H), where H denotes a Hilbert C⁎-module. First, we obtain a characterization for the system of translates {Tkϕ:k∈Z} to be a frame sequence. Then we investigate the system of generalized translates GJ associated with a...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2024-11, Vol.539 (2), p.128557, Article 128557
Main Authors: Biswas, M.H.A., Radha, R.
Format: Article
Language:English
Subjects:
Dual frame
Fiber map
Frame
Hilbert [formula omitted]-module
Semi-discrete frame
System of translates
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Summary:In this paper, we investigate three types of problems dealing with frames in L2(Rn,H), where H denotes a Hilbert C⁎-module. First, we obtain a characterization for the system of translates {Tkϕ:k∈Z} to be a frame sequence. Then we investigate the system of generalized translates GJ associated with a non-singular matrix D. Here we obtain a characterization for GJ to be a frame for L2(Rn,H). Given two systems of such translates, we obtain a necessary and sufficient condition for such systems to form a pair of dual frames. Finally, we study semi-discrete frames for L2(Rn,H), where H is a separable Hilbert space.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2024.128557