On the spectral synthesis property and its application to partial differential equations

LetM be a (n?1)-dimensional manifold inR ⁿ with non-vanishing Gaussian curvature. Using an estimate established in the early work of the author 4], we will improve the known result of Y. Domar on the weak spectral synthesis property by reducing the smoothness assumption upon the manifoldM. Also as an application of the method, a uniqueness property for partial differential equations with constant coefficients will be proved, which for some specific cases recovers or improves Hörmander's general result.