论文标题
分配的原理价值和标准扩展
On Principal Value and Standard Extension of Distributions
论文作者
论文摘要
对于复杂歧管上的全态函数f，我们在本文中解释说与| f |相关的分布2 $α$（log | f | 2）q f -n通过对集合的相应限制{| f | $ \ ge $ $ $ $ε$}当$ε$达到0时，（$α$）非负面和q，n $ \ in $ n，其值为$λ$ = $ = $ = $α$的分布的meromorthic扩展| f | 2 $λ$（log | f | 2）q f -n。这意味着由该分布生成的d module中的任何分布都具有标准扩展属性。这意味着该分布产生的D M模块的非扭转结果。作为此结果的应用，我们确定了与z（$σ$）$λ$相关的常规全体d模块的共轭模块的发生器，其中$λ$，其中$λ$是任何复杂数字，是（多值）k，z k k j = 1（-1（-1（-1（-1（-1（-1（-1（-1（-1（-1（-1），多）），多））''''s z k k k k-H z k-H-H = 0 wort IS [4 s k k-k-H = 0]
For a holomorphic function f on a complex manifold M we explain in this article that the distribution associated to |f | 2$α$ (Log|f | 2) q f --N by taking the corresponding limit on the sets {|f | $\ge$ $ε$} when $ε$ goes to 0, coincides for ($α$) non negative and q, N $\in$ N, with the value at $λ$ = $α$ of the meromorphic extension of the distribution |f | 2$λ$ (Log|f | 2) q f --N. This implies that any distribution in the D Mmodule generated by such a distribution has the Standard Extension Property. This implies a non torsion result for the D M-module generated by such a distribution. As an application of this result we determine generators for the conjugate modules of the regular holonomic D-modules associated to z($σ$) $λ$ , the power $λ$, where $λ$ is any complex number, of the (multivalued) root of the universal equation of degree k, z k + k j=1 (--1) h $σ$ h z k--h = 0 whose structure is studied in [4].
