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

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

2010-03-23

arxiv.org/abs/1003.4330v5

Differential and Integral Equations, Vol. 24 (2011), 209-230

Mathematics

Analysis of PDEs

v5, 22 pages. Basically, I have added one remark, two citations, and three sentences, revised two remarks, and also corrected

Scientific paper

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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