Algebraic Analysis of Boundary Value Problems

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(I) Microfunctions with holomorphic parameters can be restricted with respect to a holomorphic parameter. Then a natural question arises. If all the trace with respect to a holomorphic parameters, is the microfunction with holomorphic parameters is equal to zero? I gave a solution of this question positively with O. Liess and Y. Okada.(II) The 2-hyperfunctions is a natural object when we study 2^<nd> microlocalization. It contains a sheaf of microfunctions restricted to a regular involutive submanifold. I have characterized the gap between these two sheaves by means of inverse Fourier transformation.(III) Let us consider the O-solution complex of a coherent D-module M. Then it is already well studied by Y. Laurent and T. Monteiro that the vanishing cycle of M can be used to construct a boundary value morphism. I studied the relation of their result with my former result on micro-hyperbolic problems.