Ultradifferentiable extension theorems: a survey
arXiv:2107.01061 · doi:10.1016/j.exmath.2021.12.001
Abstract
We survey ultradifferentiable extension theorems, i.e., quantitative versions of Whitney's classical extension theorem, with special emphasis on the existence of continuous linear extension operators. The focus is on Denjoy-Carleman classes for which we develop the theory from scratch and discuss important related concepts such as (non-)quasianalyticity. It allows us to give an efficient and, to a fair extent, elementary introduction to Braun-Meise-Taylor classes based on their representation as intersections and unions of Denjoy-Carleman classes.
arXiv comment71 pages; many typos and minor inconsistencies corrected; to appear in Expositiones Mathematicae
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