Generalized Eigenfunctions for critical potentials with small perturbations

TL;DR

This paper analyzes how the generalized eigenfunctions of critical Dirac operators behave under small potential perturbations, with implications for similar differential operators like Schrödinger operators.

Contribution

It provides estimates for the behavior of eigenfunctions of critical Dirac operators with small potential perturbations, extending to other operators such as Schrödinger.

Findings

Eigenfunctions' behavior under small perturbations estimated

Results applicable to Schrödinger operators

Enhanced understanding of critical operator perturbations

Abstract

We estimate the behavior of the generalized eigenfunctions of critical Dirac operators (which are Dirac operators with eigenfunctions and/or resonances for $E=m$) plus small perturbations in the potential. The results also apply for other differential operators (for example Schr\"odinger operators).