High frequency resolvent estimates for perturbations by large long-range magnetic potentials and applications to dispersive estimates

TL;DR

This paper establishes optimal high-frequency resolvent estimates for Laplacian perturbations with large long-range magnetic and electric potentials, and applies these results to derive dispersive estimates for the wave group in three dimensions.

Contribution

It provides the first optimal high-frequency resolvent estimates for large long-range magnetic and electric potentials in all dimensions n≥3.

Findings

Optimal resolvent estimates proven for all dimensions n≥3.

Dispersive estimates for the wave group established in 3D.

Results enhance understanding of magnetic perturbations in dispersive PDEs.

Abstract

We prove optimal high-frequency resolvent estimates for perturbations of the Laplacian by large long-range magnetic and electric potentials in all dimensions $n\ge 3$. As an application, we prove dispersive estimates for the corresponding wave group in the case $n=3$.