High Energy Decay And Low Energy Expansion Of The Resolvent Of Fourth-order Schrodinger Operator

In this paper we study the high-energy decay estimates of the resolvent and its derivatives of operator (-△)2+V, as well as its low-energy asymptotic ex-pansions in special weighted spaces. In the third chapter, we calculate an integral representation for the resolvent by the Cauchy residue theorem. In the fifth chap-ter; we first split the free resolvent into two parts, and then obtain the high-energy estimates of free resolvent which we study in this paper by applying the estimates of free resolvent of the Schrodinger operator. What’s more, we can get the high-energy decay estimates of arbitrary order derivatives of perturbed resolvent through the relationship between free resolvent and perturbed resolvent and the recurrence relation between higher order derivative of resolvent and lower order derivative of resolvent. In the end, we expand the perturbed resolvent with low-energy in the weighted space with special weighting function.