B-Gabor type frames in separable Hilbert spaces

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.

Keywords

• gabor frame
• frame operator
• translation
• modulation