Global estimates of fundamental solutions for higher-order Schrödinger equations (Q1762466)

The authors establish global pointwise time-space estimates of the fundamental solution for Schrödinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial \[ \frac{\partial u}{\partial t}=i P(D)u,u(0,\cdot)=u_0\in L^p(\mathbb R^n)\,. \] Such estimates are used to establish related \(L^p\)-\(L^q\) estimates on the Schrödinger solution. These estimates extend known results from the literature and are sharp.