Sharp Estimates for Blowing Down Functions in a Denjoy-Carleman Class

André Belotto da Silva, Edward Bierstone, Avner Kiro

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)9685-9707
Number of pages23
JournalInternational Mathematics Research Notices
Volume2022
Issue number13
DOIs
StatePublished - 1 Jul 2022
Externally publishedYes

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