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

Abstract

LetM be a (n−1)-dimensional manifold in Rⁿ 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 manifold M. 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.