Sharp Strichartz type estimates for the Schr\"{o}dinger equation associated with harmonic oscillator

TL;DR

This paper establishes sharp Strichartz estimates for the Schrödinger equation linked to the harmonic oscillator, providing simplified proofs based on spectral projection norms and highlighting the optimal regularity conditions.

Contribution

It introduces simplified proofs for sharp Strichartz estimates for the harmonic oscillator Schrödinger equation using spectral projection norms.

Findings

Strichartz estimates are sharp in regularity

Proofs rely on $L^2 o L^p$ spectral projection bounds

Results improve understanding of initial data regularity requirements

Abstract

In this article we study the Schr\"odinger equation associated with Harmonic oscillator in the form of Strichartz type inequality. We give simple proofs for Strichartz type inequalities using purely the $L^2 \to L^p$ operator norm estimates of the spectral projections associated harmonic oscillator proved in \cite{KT}. Our Strichartz type estimates are sharp in sense of regularity of initial data.