Boundary value problem for Hyperfunction solutions to Fuchsian systems (Algebraic analytic methods in complex partial differential equations)

Abstract

In the framework of algebraic analysis, a general boundary value morphism is defined for any hyperfunction solutions to the Fuchsian system of analytic linear partial differential equations in derived category, and the injectivity of this morphism in zero-th cohomologies (that is, the Holmgren type theorem) is proved. Moreover, under a kind of hyperbolicity condition, it is proved that this morphism is surjective (that is, the solvability). These results extend that of H. Tahara and Laurent-Monteiro Fernandes to general Fuchsian systems.