Classical Proofs Of Kato Type Smoothing Estimates for The Schrödinger Equation with Quadratic Potential in R^n+1 with application
arXiv:1003.4330
Abstract
This paper applies Hermite function techniques to give elementary proofs of Kato type smoothing estimates for the Schrödinger 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.
v5, 22 pages. Basically, I have added one remark, two citations, and three sentences, revised two remarks, and also corrected two typos. Comments are welcomed. v3 was accepted to appear in Differential and Integral Equations on 04/22/2010. I think that this is the final version of the paper