 Holmgren uniqueness theorem

For a linear differential operator with real analytic coefficients, a classical solution with zero Cauchy data on a real analytic non-characteristic hypersurface vanishes locally near that hypersurface. The solution itself need not be real analytic. A proof solves the real analytic inhomogeneous formal adjoint problem against polynomial sources, annihilates all polynomial moments using boundary jets, and uses polynomial density to force the solution to vanish.