Global estimates of fundamental solutions for higher-order Schrodinger equations

In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schrodinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial. Then we use such estimates to establish related L (p) -L (q) estimates on the Schrodinger solution. These estimates extend known results from the literature and are sharp. This result was lately already generalized to a degenerate case (cf. [4]).