Dispersive Estimates for Scalar and Matrix Schr\"odinger operators on $\mathbb{H}^{n+1}$

TL;DR

This paper investigates resolvent estimates, spectral properties, and dispersive behaviors of scalar and matrix Schrödinger operators on hyperbolic spaces, providing insights into their long-term evolution and spectral structure.

Contribution

It offers new resolvent estimates and dispersive analysis for Schrödinger operators on hyperbolic spaces, extending previous Euclidean results to non-compact symmetric spaces.

Findings

Derived resolvent estimates for Schrödinger operators on hyperbolic spaces

Established dispersive decay rates for solutions over time

Analyzed spectral properties of scalar and matrix operators

Abstract

We study resolvent estimates, spectral theory and long time dispersive properties of scalar and matrix Schr\"odinger-type operators on $\mathbb{H}^{n+1}$ for $n \geq 1$.