Asymptotic Behaviour of the Scattering Phase for Non-Trapping Metrics

摘要

The asymptotic behaviour of the scattering phase is considered at infinity for an elliptic, self-adjoint, second order differential operator H, defined either in Rsup(n) or in an unbounded domain omega contains Rsup(n) with Dirichlet or Neumann boundary conditions. The operator H has the form H=- delta sub(g)+hD+V where delta sub(g) is the Laplace-Beltrami operator related to a Riemann metric g in anti omega . Provided a non-trapping hypothesis is fulfilled and H coincides with the Laplace operator delta in a neighbourhood of infinity, an asymptotic development of the scattering phase s(lambda) is obtained for lambda implies infinity. The first coefficients in this development are found. (Atomindex citation 14:780551)