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

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.

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