Local energy decay for wave equation in the absence of resonance at zero energy in 3D

TL;DR

This paper investigates spectral properties of Schrödinger operators with exponentially decaying potentials in 3D, establishing local energy decay for wave solutions and absence of zero-energy resonances in NLS.

Contribution

It introduces new spectral analysis results for Schrödinger operators with exponential decay, leading to proofs of local energy decay and resonance absence.

Findings

Proves local energy decay for wave equations with exponential potentials.

Shows absence of zero-energy resonances for NLS.

Provides spectral characterization in 3D with exponential decay.

Abstract

In this paper we study spectral properties associated to Schrodinger operator with potential that is an exponential decaying function. As applications we prove local energy decay for solutions to the perturbed wave equation and lack of resonances for the NLS.