Algebraic Analysis of Boundary Value Problems

(1)具有全纯参数的微函数可以被一个全纯参数所限制。那么一个自然的问题就出现了。如果所有关于全纯参数的迹，具有全纯参数的微函数是否等于零？我与O. Liess和Y. Okada积极地给出了这个问题的解决方案。（II） 2-超功能是研究2^<和>微定位的自然对象。它包含一组被限制在正则对合子流形中的微函数。我已经用傅里叶反变换描述了这两个轴之间的间隙。(3)我们考虑一个相干d模M的o解复形，那么Y. Laurent和T. Monteiro已经很好地研究了M的消失环可以用来构造一个边值态射。我研究了他们的结果与我先前关于微双曲问题的结果的关系。

(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.