On Weyl-Heisenberg Frames

TL;DR

This paper generalizes Weyl-Heisenberg frames to include a bounded linear operator K, providing necessary and sufficient conditions for such frames and exploring their invariance properties.

Contribution

It introduces the concept of K-Weyl-Heisenberg frames, extending classical frames with new conditions and invariance properties.

Findings

Derived necessary and sufficient conditions for K-Weyl-Heisenberg frames.

Established invariance properties of these frames.

Generalized the classical frame theory to operator-based systems.

Abstract

In this paper we have generalized and studied the $K$-Weyl-Heisenberg frames, where $K$ is a bounded linear operator on $L^2(\mathbb{R}^d)$. We have obtained necessary and sufficient conditions for acertain system to be a $K$-Weyl-Heisenberg frame. We have also given the invariance property of these $K$-Weyl-Heisenberg frames.