The Classification Of Resonances And Kato-Jensen Estimates Of A Class Of Higher-order Schrodinger Operators

In this paper,we study the decay estimates of the sixth-order Schrodinger op-erator H=(-?)3+V(x)in R5.We establish the Kato-Jensen estimates of the sixth-order Suhrodinger group e-it((-?3)+V(x))with respect to time t in the suitable decay conditions of V(x).Related estimates play an important role in the well-posed study of solutions of nonlinear higher-order Schrodinger equation.The paper is organized as follows:Firstly,in the free case,we give the asymptotic expansions of the resolvent R0(z)=((-?)3-z)-1 near the origin.In the potential perturbed case,according to the classification of resonances of the operator H near the origin,we get the detail lower energy expansions of the perturbed resolvent Rv(z)=(H-z)-1 in the corresponding cases by the symmetric resolvent identity.Secondly,we establish the relationship between the spectral subspaces SiL2 for i=1,2,3,4 and distributional solutions to H?=0,moreover we obtain the higher energy decay estimates and limiting absorption principle of the perturbed resolvent RV(z).Finally,we obtain the lower energy expansions and higher energy decay estimates of spectral measures by Stone's formula,moreover we prove the Kato-Jensen estimates of the sixth-order Schrodinger;group e-itH in the corresponding resonances case.