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arXiv · 2107.01061

Ultradifferentiable extension theorems: a survey

Armin Rainer
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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.

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Armin Rainer. 2021-07-02. Ultradifferentiable extension theorems: a survey. https://doi.org/10.1016/j.exmath.2021.12.001

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