On a class of linear differential operators of infinite order with finite index
On a class of linear differential operators of infinite order with finite index
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关于一类无限阶有限索引线性微分算子
DOI：
10.1016/0001-8708(86)90098-8
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发表时间：
1986
影响因子：
1.7
通讯作者：
T. Kawai
中科院分区：
文献类型：
--
作者：
T. Aoki;M. Kashiwara;T. Kawai
无限阶微微分算子理论的最新进展[1 -4]及其在几个分析分支[IS，11，16-241]中的有用性增强了对此类算子的兴趣。然而，我们的知识，这样的运营商仍然是相当有限的，特别是与我们的知识相比，有限阶的运营商。例如，我们不知道很多关于这样一个基本问题，作为特征的线性微分算子的无限级，这是封闭的范围作为一个映射，从芽的全纯函数芽的全纯函数。据我们所知，Ishimura最近的工作[7]是唯一具有一定普遍适用性的结果，尽管它离最终目标还很远。本文的目的是证明一些定理，希望对这类算子的研究有所贡献。具体地说，我们给出了线性微分算子P的一些条件，这些条件保证了映射P的核和上核维数的有限性：Ccn，o-+ O，，，，，其中Ocn，O表示层0，，的原点芽. C上的全纯函数：特别地，在这些条件下，映射具有有限指数，并且是闭值域的（定理4和定理5）。我们的结果是Bony和Schapira [S，Thtoreme 5.11]对无穷阶情形的自然推广.它也非常类似于Kashiwara，Kawai和Sjostrand [12]在其哲学意义上，适当选择切向系统的某些椭圆度条件位于155
The recent progress of the theory of microdifferential operators of infinite order [l-4] and their usefulness in several branches of analysis [IS, 11, 16-241 have enhanced the interest in such operators. However, our knowledge on such operators is still quite limited, particularly compared with our knowledge on operators of finite order. For example, we do not know much about such a basic problem as characterizing a linear differential operator of infinite order which is of closed range as a map from germs of holomorphic functions to germs of holomorphic functions. To the best of our knowledge, Ishimura’s recent work [7] is the only result that has some general applicability, although it is still far from the final goal. The purpose of this paper is to prove some theorems which we hope to contribute toward the progress of the study of such operators. To be concrete, we present some conditions on a linear differential operator P which guarantees the finiteness of the dimensions of the kernel and the cokernel of the map P: Ccn, o-+ O,,,,, where Ocn, O denotes the germ at the origin of the sheaf 0,. of holomorphic functions on C:“. In particular, under those conditions the map has finite index, and it is of closed range (Theorem 4 and Theorem 5). Our results are a natural generalization of Bony and Schapira [S, Thtoreme 5.11 to the infinite-order case. It is also quite akin to Kashiwara, Kawai, and Sjostrand [12] in its philosophy in the sense that some ellipticity condition for a suitably chosen tangential system lies 155
（偏）微分算子的中间卷积
DOI：
--
发表时间：
2009
期刊：
影响因子：
--
作者：
Kentaroh Watanabe;Kensuke Wada;Hidehiro Kaneda;Kensuke Ide;Masahiro Kato;Takehiko Wada;K. Ishige and T. Kawakami;平沢和司;水谷勉・尾崎久記・小池敏英;Nariya Kawazumi;大島利雄
通讯作者：
大島利雄