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arXiv · 1003.4330

Classical Proofs Of Kato Type Smoothing Estimates for The Schr\"odinger Equation with Quadratic Potential in R^n+1 with application

Xuwen Chen
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Abstract

This paper applies Hermite function techniques to give elementary proofs of Kato type smoothing estimates for the Schr\"odinger equation with quadratic potential in R^n+1. This is equivalent to proving a uniform L^2(R^n) to L^2(R^n) boundedness for a family of singularized Hermite projection kernels. As an applicationas the above estimate, we also prove the R^9 collapsing variable type Strichartz estimate.

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Xuwen Chen. 2010-03-23. Classical Proofs Of Kato Type Smoothing Estimates for The Schr\"odinger Equation with Quadratic Potential in R^n+1 with application. https://arxiv.org/abs/1003.4330

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