On the spectral synthesis property and its application to partial differential equations
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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 , 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.
KeywordsPartial Differential Equation Dimensional Manifold Lorentz Space Smoothness Assumption Spectral Synthesis
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