Some Types of Linear Combinations of Weyl-Heisenberg Wave Packet Frames Over Local Fields of Positive Characteristic

TL;DR

This paper establishes conditions under which certain linear combinations of Weyl-Heisenberg wave packet frames form new frames in the context of local fields of positive characteristic, expanding frame theory in non-Archimedean settings.

Contribution

It provides necessary and sufficient criteria for linear combinations of wave packet frames to be frames over local fields of positive characteristic, a novel extension in frame theory.

Findings

Derived explicit conditions for frame preservation under linear combinations

Extended frame theory to local fields of positive characteristic

Enhanced understanding of wave packet frames in non-Archimedean analysis

Abstract

In this paper, we present necessary and sufficient conditions for some types of linear combination of frame elements (wave packet) to be a frame for $L^2(\mathbb{K})$, where $\mathbb{K}$ is a local field of positive characteristic.