Global estimates of fundamental solutions for higher-order Schr\"odinger   equations
  In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schr\"odinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial. Then we use such estimates to establish related Lp-Lq estimates on the Schr\"odinger solution. These estimates extend known results from the literature and are sharp. This result was latetly already generalized to a degenerate case (cf. [9]). 
JinMyong Kim, Anton Arnold and Xiaohua Yao
math.AP math-ph math.MP