Commutator Algebra and Resolvent Estimates

Abstract

In studying the detailed properties of Schrodinger operators, the method of micro-localization seems to be indispensable.For the manybody problem, this point of view was introduced by Enss [3], Mourre [11] and then by to investigate the propagation properties of the unitary group.These sorts of estimates not only lead us to a deep understanding of the space-time behavior of the solution to the Schrodinger equation, but also give us many applications.The aim of this paper is to prove a certain variation of these kinds of estimates for the resolvent of the N-body Schrodinger operator.We consider a system of N-particles moving in Rv with mass mi and position xi E Rv(l