$L^p$ resolvent estimates for magnetic Schr\"odinger operators with unbounded background fields

TL;DR

This paper establishes $L^p$ resolvent and smoothing estimates for magnetic Schr"odinger operators with unbounded background fields, and applies these results to eigenvalue location problems for complex electromagnetic potentials.

Contribution

It introduces new $L^p$ resolvent estimates for magnetic Schr"odinger operators with unbounded backgrounds, extending previous results to more general electromagnetic potentials.

Findings

Proved $L^p$ resolvent estimates for magnetic Schr"odinger operators.

Derived eigenvalue location estimates for operators with complex potentials.

Extended analysis to operators with unbounded background electromagnetic fields.

Abstract

We prove $L^p$ and smoothing estimates for the resolvent of magnetic Schr\"odinger operators. We allow electromagnetic potentials that are small perturbations of a smooth, but possibly unbounded background potential. As an application, we prove an estimate on the location of eigenvalues of magnetic Schr\"odinger and Pauli operators with complex electromagnetic potentials.