Dilation-analytic wave operators for three particles (Q1822025)

Let H be the Hamiltonian of a system of three nonrelativistic particles, in the center of mass frame, interacting through dilation analytic potentials. Then H is embedded into a holomorphic family of operators with the same domain. Let H(\(\phi)\) be the operator obtained after analytic continuation with an angle \(\phi\). In a preceding paper the author proved the existence of wave operators \(W(\pm,a,\phi)\), where a is either zero or the energy of a two-body bound state, such that [H(\(\phi)\)-a] \(W(\pm,a,\phi)=-W(\pm,a,\phi)\Delta (a)e^{2i\phi}\). Here \(\Delta\) (a) is the kinetic energy in the channel defined by a. In this paper the operators W are studied and it is shown that they send analytic functions of the coordinates into analytic functions.