Microlocal boundary value problem for regular-specializable systems

Abstract

In the framework of microlocal analysis, a boundary value morphism is defined for solutions to the regular-specializable system of analytic linear partial differential equations. This morphism can be regarded as a microlocal counterpart of the boundary value morphism for hyperfunction solutions due to Monteiro Fernandes, and the injectivity of this morphism (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).