Kohn算法在实解析情形下终止性的直接证明
Direct Proof of Termination of the Kohn Algorithm in the Real-Analytic Case
AI总结：
本文给出Kohn算法在实解析边界伪凸域上终止性的直接证明，利用边界系统分层与实解析代数几何，并探讨计算亚椭圆增益下界的途径。
摘要：
1979年，J.J. Kohn通过Diederich-Fornæss定理给出了一个间接论证，表明对于具有实解析边界的伪凸域，有限的D'Angelo类型蕴含Kohn算法的终止性。本文利用Catlin的边界系统概念所导出的分层结构，以及实解析函数环上的代数几何，为该蕴含关系提供了一个直接论证。我们还指出，若能在实解析情形下证明有效的Łojasiewicz不等式，并获得关于Kohn算法中乘子层行为的更多信息，则该论证可用于计算$\bar\partial$-Neumann问题中亚椭圆增益的有效下界，该下界以D'Angelo类型、空间维度和形式层次表示。
英文摘要：
In 1979 J.J. Kohn gave an indirect argument via the Diederich-Fornæss Theorem showing that finite D'Angelo type implies termination of the Kohn algorithm for a pseudoconvex domain with real-analytic boundary. We give here a direct argument for this same implication using the stratification coming from Catlin's notion of a boundary system as well as algebraic geometry on the ring of real-analytic functions. We also indicate how this argument could be used in order to compute an effective lower bound for the subelliptic gain in the $\bar\partial$-Neumann problem in terms of the D'Angelo type, the dimension of the space, and the level of forms provided that an effective Łojasiewicz inequality can be proven in the real-analytic case and slightly more information obtained about the behavior of the sheaves of multipliers in the Kohn algorithm.
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