Heisenberg-Pauli-Weyl and Donoho-Stark's uncertainty principle for the Weinstein $L^2$-multiplier operators

TL;DR

This paper extends classical uncertainty principles to Weinstein $L^2$-multiplier operators, establishing foundational bounds that connect time and frequency localization in this context.

Contribution

It introduces the Heisenberg-Pauli-Weyl and Donoho-Stark uncertainty principles specifically for Weinstein $L^2$-multiplier operators, a novel application in harmonic analysis.

Findings

Established the Heisenberg-Pauli-Weyl uncertainty principle for Weinstein $L^2$-multipliers.

Proved Donoho-Stark's uncertainty principle in the Weinstein setting.

Provided new bounds linking localization properties in this operator framework.

Abstract

The aim of this paper is establish the Heisenberg-Pauli-Weyl uncertainty principle and Donho-Stark's uncertainty principle for the Weinstein $L^2$-multiplier operators.