Sharp estimates for the Schr\"odinger equation associated to the twisted Laplacian

TL;DR

This paper derives Strichartz estimates for the Schr"odinger equation linked to the twisted Laplacian on complex space, using Sobolev spaces tailored to this operator, advancing understanding of its dispersive properties.

Contribution

It provides new sharp Strichartz estimates for the Schr"odinger equation with the twisted Laplacian, a less-studied operator in harmonic analysis.

Findings

Established Strichartz estimates for the twisted Laplacian Schr"odinger equation.

Identified suitable Sobolev spaces for initial data analysis.

Enhanced understanding of dispersive properties of the twisted Laplacian.

Abstract

In this note we obtain some Strichartz estimates for the Schr\"odinger equation associated to the twisted Laplacian on $\mathbb{C}^{n}\cong \mathbb{R}^{2n}$. The initial data will be considered in suitable Sobolev spaces associated to the twisted Laplacian.