B-Gabor type frames in separable Hilbert spaces

Authors

  • Thomas Jineesh Mahatma Gandhi University Kerala India
  • N M Madhavan Namboothiri Mahatma Gandhi University Kerala India
  • P N Jayaprasad Mahatma Gandhi University Kerala India

DOI:

https://doi.org/10.23755/rm.v48i0.1236

Keywords:

Gabor frame, frame operator, translation, modulation

Abstract

It is guaranteed that Gabor like structured frames do exist in any finite dimensional Hilbert space via an invertible map from l2(ZN) J Thomas and Nambudiri [2022]. Hence the question: whether it is possible to obtain structured class of frames in separable Hilbert spaces? is relevant. In this article we obtain a structured class of frames for separable Hilbert spaces which are generalizations of Gabor frames for L2(R) in their construction aspects. We call them as B-Gabor type frames and present a characterization of the frame operators associated with these frames when B is a unitary map. Some significant properties of the associated frame operators are discussed.

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Published

2023-12-30

Issue

Vol. 48 (2023)

Section

Volume 48-2023

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