Sharp Estimates for Blowing Down Functions in a Denjoy-Carleman Class
Complex Variables
2020-11-30 v2 Algebraic Geometry
Classical Analysis and ODEs
Abstract
If F is an infinitely differentiable function whose composition with a blowing-up belongs to a Denjoy-Carleman class C_M (determined by a log convex sequence M=(M_k)), then F, in general, belongs to a larger shifted class C_N, where N_k = M_2k; i.e., there is a loss of regularity. We show that this loss of regularity is sharp. In particular, loss of regularity of Denjoy-Carleman classes is intrinsic to arguments involving resolution of singularities.
Cite
@article{arxiv.2006.10580,
title = {Sharp Estimates for Blowing Down Functions in a Denjoy-Carleman Class},
author = {André Belotto da Silva and Edward Bierstone and Avner Kiro},
journal= {arXiv preprint arXiv:2006.10580},
year = {2020}
}
Comments
V2: minor corrections. To appear in IMRN. 16 pages