A uniqueness result in an inverse hyperbolic problem with analyticity

We prove the uniqueness for the inverse problem of determining a coefficient q(x) in (partial defferential)2_t u(x,t) = (Delta) u(x,t) - q(x)u(x,t) for x (element of) R^n and t > 0, from observations of u|(Gamma)*(0,T) and the normal derivative (partial defferential) u/(partial defferential)(nu)|(Gamma)*(0,T) where (Gamma) is an arbitrary C^(infinity)-hypersurface. Our main result asserts the uniqueness of q over R^n provided that T > 0 is sufficiently large and q is analytic near (Gamma) and outside a ball. The proof depends on Fritz Johnʹs global Holmgren theorem and the uniqueness by a Carleman estimate.