The Kohn Algorithm on Denjoy-Carleman Classes

Details The Kohn Algorithm on Denjoy-Carleman Classes The Kohn Algorithm on Denjoy-Carleman Classes

2008-06-11

arxiv.org/abs/0806.1917v3

Mathematics

Complex Variables

18 pages, submitted to the International Journal of Mathematics; revision according to referee reports

Scientific paper

The equivalence of the Kohn finite ideal type and the D'Angelo finite type with the subellipticity of the dbar-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 non-Noetherian and 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 ascending chain condition on self-radical ideals property, one of the strongest properties a non-Noetherian ring could possess.

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