Author

Guiyu Xie

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Preprint Aug 2026

Sharp Endpoint Eigenfunction Estimates for the Two-Dimensional Hermite Operator

Let $\mathcal H=-\Delta+|x|^2$ be the Hermite operator on $\mathbb R^2$, and let $\Pi_\lambda$ denote the spectral projection corresponding to $\lambda=2N+2$. We prove the sharp log-free endpoint estimate $||\Pi_\lambda||_{L^2(\mathbb R^2)\to L^{10/3}(\mathbb R^2)}\lesssim\lambda^{-1/10}$. The proof uses a spectral dec...

Guiyu Xie, Cheng Zhang · 0 citations