Restriction theorem for the Fourier–Hermite transform and solution of the Hermite–Schrödinger equation

Abstract

In this article, we prove a restriction theorem for the Fourier–Hermite transform and obtain a Strichartz estimate for the system of orthonormal functions for the Hermite operator $$H=-\Delta +|x|^2$$ on $${\mathbb {R}}^n$$ as application. Further, we show the optimal behavior of the constant in the Strichartz estimate as limit of a large number of functions.