Bounds on the Hermite spectral projection operator

Eunhee Jeong, Sanghyuk Lee, Jaehyeon Ryu

We study $L^p$-$L^q$ bounds on the spectral projection operator ${\Pi }_{\lambda }$ associated to the Hermite operator $H=|x{|}^2-\Delta$ in ${\mathbb{R}}^d$. We are mainly concerned with a localized oper…