Semi-continuous g-frames in Hilbert spaces

TL;DR

This paper introduces semi-continuous g-frames in Hilbert spaces, explores their structure via Fourier transform, and demonstrates their stability and fundamental properties, expanding the theoretical framework of frame theory.

Contribution

It defines semi-continuous g-frames, constructs examples using Fourier transforms of the Heisenberg group, and proves their stability under perturbations.

Findings

Constructed semi-continuous g-frames using Fourier transform

Derived fundamental identities and inequalities for these frames

Proved stability of semi-continuous g-frames under small perturbations

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.