2008/06/11 by Nicoara, Andreea C.
#13E99 #26E10 (Primary) 46E25 #32T25 (Secondary) #32W05 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.0806.1917
The equivalence of the Kohn finite ideal type and the D'Angelo finite type with the subellipticity of the ∂-Neumann problem is extended to pseudoconvex domains in Cn 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 √(acc) property, one of the strongest properties a non-Noetherian ring could possess.