Jordan decomposition for a class of singular differential operators
Jordan decomposition for a class of singular differential operators
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DOI：
10.1007/bf02386195
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发表时间：
1975-12
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影响因子：
--
通讯作者：
A. Levelt
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文献类型：
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作者：
A. Levelt
众所周知，Turrittin的证明基本上可以通过使用循环向量来简化。这样的证明同样可以得到p的估计：例如p= n！就足够了这一点在Turrittin的定理（参见[2]，第7页）中是没有的。然而，还有另一个空白，即关于独特性的声明。填补这一空白是本文件的主要目的。在这里，又一个众所周知的线性变换分解成一个半单变换和一个幂零变换的和可以被模仿。这导致了第1节定理I和II的主要结果。
As is more or less known Turrittin's proof can essentially be simplified by using cyclic vectors. Such a proof can equally lead to an estimate of p: for instance p= n! will suffice. This point was missing in Turrittin's theorem (cf [2], p. 7). However, there is still another gap, namely a statement on uniqueness. Filling this gap is the main purpose of the present paper. Here again the well-known decomposition of a linear transformation into the sum of a semisimple transformation and a nilpotent one can be imitated. This leads to the main results the Theorems I and II of section 1.