Some Studies On Dispersive Estimates Of Higher-order Elliptic Operators

In this paper,we study the decay estimates of the higher-order elliptic operators H =(-?)m+ V(x)with m?2(m ?N)in Rn for n>2m.Our main goals are to establish the Kato-Jensen estimates,local decay estimates and the Strichartz estimates of higher-order Schr(?)dinger group e-it(-?)m+V(x)).According to the low energy asymptotic expansions and the high energy decay estimates of the resolvent RV(z),we obtain the estimates of spectral measures by Stone's formula,then we prove the Kato-Jensen estimates.As an corollary of the uniform estimates of resolvent,we get the local decay estimates of(-?)m + V(x).Finally,according to the Kato-Jensen estimates and local decay estimates,combining with the dispersive estimates of the free higher-order Schr(?)dinger group e-it(-?)m,we establish the endpoint Strichartz estimates of e-it((-?)m+V(x)).