On the holonomic systems of linear differential equations, II
On the holonomic systems of linear differential equations, II
复制标题
关于线性微分方程的完整系统，II
DOI：
10.1007/bf01403082
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发表时间：
1978
影响因子：
3.1
通讯作者：
M. Kashiwara
中科院分区：
文献类型：
--
作者：
M. Kashiwara
在本文中，我们将研究对微分方程的自动系统的限制。令x为复杂的歧管，y submanifold，让（9 x和d x分别为有限顺序的差异算子的捆绑符。方程式，对y的限制也满足X上系统的微分方程的系统。这导致了以下定义根据定义，〜/o n t o y的限制是（gr | j //。但是，如果y是特征，则限制不再是相干的。 。是不连贯的。
In this paper we shall study the restriction of holonomic systems of differential equations. Let X be a complex manifold and Y a submanifold, and let (9 x and D x be the sheaf of the holomorphic functions and the sheaf of the differential operators of finite order, respectively. If a function u on X satisfies a system of differential equations, the restriction of u onto Y also satisfies the system of differential equations derived from the system on X. This leads to the following definition. Let JC{ be a Dx-Module. The restriction of ~ / o n t o Y is, by definition, (gr | J//. ~x In [4] it is proved that if Jr is a coherent Dx-Module and if Y is noncharacteristic to Jg, then the restriction of Jg is also a coherent Dr-Module. However, if Y is characteristic, the restriction is no longer coherent in general. For examples, if X=II2" and Y = { x = ( x 1 . . . . , x , ) eX ; x l = O } and J g = D x , the restriction JC[/xlJCl is a free Dr-Module generated by D~(m=0, 1,2,...) and is not coherent. We shall prove the following theorems in this paper.