Estimates in the modulation spaces for the Dirac equation with potential

TL;DR

This paper derives estimates in modulation spaces for solutions to the Dirac equation with quadratic and sub-quadratic potentials, using a new representation of the Dirac operator for approximate solutions.

Contribution

It introduces a novel representation of the Dirac operator enabling estimates in modulation spaces for equations with certain potentials.

Findings

Established modulation space estimates for Dirac solutions

Provided a new representation for the Dirac operator

Achieved approximate solutions for perturbed Dirac equations

Abstract

In the present paper we obtain estimates in the modulation spaces for the solutions to the Dirac equation with quadratic and sub-quadratic potentials. We derive a representation for the Dirac operator that permits to solve approximately the perturbed Dirac equation and to obtain the desired estimates for the solution.