Semi-continuous g-frames in Hilbert spaces

Abstract

In this paper, we introduce the concept of semi-continuous $g$-frames in Hilbert spaces. We first construct an example of semi-continuous $g$-frames using the Fourier transform of the Heisenberg group and study the structure of such frames. Then, as an application we provide some fundamental identities and inequalities for semi-continuous $g$-frames. Finally, we present a classical perturbation result and prove that semi-continuous $g$-frames are stable under small perturbations.

16 pages

References in corpus (3)

• Some Identities and Inequalities for Hilbert-Schmidt Frames
• Approximation of the Inverse Frame Operator and Stability of Hilbert$-$Schmidt Frames
• Atomic decompositions for operators in reproducing kernel Hilbert spaces

Cited by in corpus (1)

• Continuous frames in tensor product Hilbert spaces, localization operators and density operators