Scattering operator for nonlinear Klein-Gordon equations in higher space dimensions

We prove the existence of the scattering operator in the neighborhood of the origin in the weighted Sobolev space H(beta, 1) with beta = max(3/2, 1 + 2/n) for the nonlinear Klein-Gordon equation with a power non-linearity u(tt) - Delta u + u = mu vertical bar u vertical bar(sigma -1)u, (t, x) epsilon R x R(n) where 1 + 4/n+2 < sigma < 1 + 4/n for n >= 3, mu epsilon C. (C) 2007 Elsevier Inc. All rights reserved.