A Beals criterion for magnetic pseudodifferential operators proved with magnetic Gabor frames

TL;DR

This paper introduces a new proof of the Beals criterion for magnetic pseudodifferential operators using magnetic Gabor frames, extending classical results to magnetic contexts.

Contribution

It provides a novel proof for the Beals criterion in magnetic settings by developing a magnetic Gabor frame approach, bridging classical and magnetic pseudodifferential operator theory.

Findings

New proof of Beals criterion for non-magnetic operators

Introduction of magnetic Gabor frames for magnetic operators

Derivation of magnetic Beals criterion using these frames

Abstract

First, we give a new proof for the Beals commutator criterion for non-magnetic Weyl pseudo-differential operators based on classical Gabor tight frames. Second, by introducing a modified 'magnetic' Gabor tight frame, we naturally derive the magnetic analogue of the Beals criterion originally considered by Iftimie-M\u{a}ntoiu-Purice.