1104.5367 (JinMyong Kim et al.)

Global estimates of fundamental solutions for higher-order Schrödinger
equations    [PDF]

JinMyong Kim, Anton Arnold, Xiaohua Yao

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]).

View original: http://arxiv.org/abs/1104.5367