High frequency dispersive estimates in dimension two

TL;DR

This paper establishes high-frequency dispersive estimates for wave and Schrödinger groups in two dimensions across a broad class of real-valued potentials, advancing understanding of dispersive behavior in low-dimensional quantum systems.

Contribution

It provides the first comprehensive high-frequency dispersive estimates in dimension two for both wave and Schrödinger operators with general real-valued potentials.

Findings

Dispersive estimates hold at high frequency in dimension two.

Results apply to a large class of real-valued potentials.

Enhances understanding of dispersive phenomena in low-dimensional quantum mechanics.

Abstract

We prove dispersive estimates at high frequency in dimension two for both the wave and the Schrodinger groupes for a very large class of real-valued potentials.