TY - JOUR
T1 - Sharp Estimates for Blowing Down Functions in a Denjoy-Carleman Class
AU - da Silva, André Belotto
AU - Bierstone, Edward
AU - Kiro, Avner
N1 - Publisher Copyright:
© The Author(s) 2021.
PY - 2022/7/1
Y1 - 2022/7/1
N2 - If F is a C∞ function whose composition F ° σ with a blowing-up σ belongs to a Denjoy-Carleman class CM, then F, in general, belongs to a larger class CM(2); that is, there is a loss of regularity. We show that this loss of regularity is sharp. In particular, the loss of regularity of Denjoy-Carleman classes is intrinsic to arguments involving resolution of singularities.
AB - If F is a C∞ function whose composition F ° σ with a blowing-up σ belongs to a Denjoy-Carleman class CM, then F, in general, belongs to a larger class CM(2); that is, there is a loss of regularity. We show that this loss of regularity is sharp. In particular, the loss of regularity of Denjoy-Carleman classes is intrinsic to arguments involving resolution of singularities.
UR - http://www.scopus.com/inward/record.url?scp=85134397919&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnaa367
DO - 10.1093/imrn/rnaa367
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85134397919
SN - 1073-7928
VL - 2022
SP - 9685
EP - 9707
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 13
ER -