On Holonomic Systems of Micro-differential Equations. III-Systems with Regular Singularities-
On Holonomic Systems of Micro-differential Equations. III-Systems with Regular Singularities-
复制标题
关于微微分方程的完整系统。
DOI：
10.2977/prims/1195184396
复制
发表时间：
1981
影响因子：
1.2
通讯作者：
T. Kawai
中科院分区：
文献类型：
--
作者：
M. Kashiwara;T. Kawai
这是关于完整系统的系列论文的第三篇。根据定义，一个完整系统是一个左相干的f模（或^-模）*，其特征变化是拉格朗日的。它与一个线性常微分方程具有有限定理，即与它的解簇相关的所有上同调群都是有限维的（[6],[12]）。因此，对这样一个系统的研究将给我们提供关于满足系统的函数的几乎完整的信息，就像在一维情况下一样。实际上，利用常微分方程理论分析特殊函数是经典分析中的重要课题之一。从这个角度来看，研究具有正则奇点的完整系统是非常重要的。然而，尽管具有规则奇异点的线性常微分方程理论已经得到了相当成功的发展，但是具有规则奇异点的完整系统的一般理论在过去并没有得到充分的发展，特别是与一维情况下取得的卓有成效的成功相比。然而，这是值得做的，我们希望我们已经为本文的理论建立了坚实的基础。例如，我们建立了具有正则奇点的完整系统的操作所需要的几个基本结果，如这类系统的积分和限制（第五章）。我们也给出了一个解析性质-
This is the third of the series of the papers dealing with holonomic systems(*. A holonomic system is, by definition, a left coherent (f-Module (or ^-Modules)* whose characteristic variety is Lagrangian. It shares the finiteness theorem with a linear ordinary differential equation, namely, all the cohomology groups associated with its solution sheaf are finite dimensional ([6], [12]). Hence the study of such a system will give us almost complete information concerning the functions which satisfy the system, as in the onedimensional case. Actually, analyzing special functions by the aid of the theory of ordinary differential equations is one of the most important subjects in the classical analysis. From this point of view, the study of holonomic systems with regular singularities is most important. However, even though the theory of linear ordinary differential equations with regular singularities has been developed quite successfully, the general theory of holonomic systems with regular singularities was not fully developed in the past, especially compared with the fruitful success attained in the one-dimensional case. Still it should be worth doing, and we hope we have established a solid basis for the theory in this paper. For example, we establish several basic results needed for the manipulation of holonomic systems with regular singularities, such as the integration and the restriction of such systems (Chapter V). We also give an analytic character-
DOI：
--
发表时间：
2006
期刊：
影响因子：
--
作者：
M.Mimura;T.Miyaji and I.Ohnishi;S.KAWANO and S.KONISIiI;T. Oshima
通讯作者：
T. Oshima