Sharp frequency bounds for eigenfunctions of the Ornstein-Uhlenbeck operator

TL;DR

This paper establishes precise bounds on the growth rates of eigenfunctions of the Ornstein-Uhlenbeck operator, with implications for geometric flows and mathematical analysis.

Contribution

It provides the first sharp bounds for eigenfunction growth rates of the Ornstein-Uhlenbeck operator, including lower order terms.

Findings

Bounds are sharp up to lower order terms.

Results have significant applications to geometric flows.

The bounds improve understanding of eigenfunction behavior.

Abstract

We prove sharp bounds for the growth rate of eigenfunctions of the Ornstein-Uhlenbeck operator and its natural generalizations. The bounds are sharp even up to lower order terms and have important applications to geometric flows.