ON THE SPECTRAL-SYNTHESIS PROPERTY AND ITS APPLICATION TO PARTIAL-DIFFERENTIAL EQUATIONS

Let M 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. © 1992 Institut Mittag-Leffler.