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arXiv 0806.19172008-06math.CVmath.AG

Denjoy-Carleman类上的Kohn算法

The Kohn Algorithm on Denjoy-Carleman Classes

Andreea C. Nicoara

备注：: 26 pages, quasicoherence argument redone in a clearer fashion
发表信息：: J. Geom. Anal. 35 (2025), no. 12, Paper No. 399

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AI总结：

本文将Kohn有限理想型与D'Angelo有限型同$\bar\partial$-Neumann问题次椭圆性的等价性推广到定义函数属于Denjoy-Carleman拟解析类的伪凸域，并证明相应的函数芽环满足$\sqrt{acc}$性质。

摘要：

Kohn有限理想型与D'Angelo有限型在$\bar\partial$-Neumann问题的次椭圆性上的等价性被推广到$C^n$中的伪凸域，其定义函数属于一个在微分运算下封闭的Denjoy-Carleman拟解析类。证明涉及在一个Denjoy-Carleman拟解析函数芽环上的代数几何，该环目前未知是否为Noether环，且介于实解析函数芽环与光滑函数芽环之间。本文还证明了这类Denjoy-Carleman函数芽环满足$\sqrt{acc}$性质，这是非Noether环所能具有的最强性质之一。

英文摘要：

The equivalence of the Kohn finite ideal type and the D'Angelo finite type with the subellipticity of the $\bar\partial$-Neumann problem is extended to pseudoconvex domains in $C^n$ whose defining function is in a Denjoy-Carleman quasianalytic class closed under differentiation. The proof involves algebraic geometry over a ring of germs of Denjoy-Carleman quasianalytic functions that is not known to be Noetherian and that is intermediate between the ring of germs of real-analytic functions and the ring of germs of smooth functions. It is also shown that this type of ring of germs of Denjoy-Carleman functions satisfies the $\sqrt{acc}$ property, one of the strongest properties a non-Noetherian ring could possess.

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