Extending cutoff resolvent estimates via propagation of singularities

TL;DR

This paper demonstrates that polynomially bounded cutoff resolvent estimates on the real axis can be extended to a neighborhood of the real axis using a propagation of singularities approach.

Contribution

It introduces a gluing method that leverages propagation of singularities to extend resolvent estimates beyond the real axis.

Findings

Resolves resolvent estimates near the real axis.

Extends polynomial bounds to neighborhoods of the real axis.

Provides a new technique for analyzing resolvent behavior.

Abstract

We use a gluing method developed in joint work with Andr\'as Vasy to show that polynomially bounded cutoff resolvent estimates at the real axis imply, up to a constant factor, the same estimates in a neighborhood of the real axis.