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arXiv · 2312.03238

Sparse systems of functions and quasi-analytic classes

Marco Aldi·Jeffrey Buffkin II·Cody Cline·Sean Cox
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Abstract

We provide a new characterization of quasi-analyticity of Denjoy-Carleman classes, related to \emph{Wetzel's Problem}. We also completely resolve which Denjoy-Carleman classes carry \emph{sparse systems}: if the Continuum Hypothesis (CH) holds, \textbf{all} Denjoy-Carleman classes carry sparse systems; but if CH fails, a Denjoy-Carleman class carries a sparse system if and only if it is not quasi-analytic. As corollaries, we extend results of \cite{MR3552748} and \cite{CodyCoxLee} about non-existence of "anonymous predictors" for real functions.

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Marco Aldi, Jeffrey Buffkin II, Cody Cline, Sean Cox. 2023-12-06. Sparse systems of functions and quasi-analytic classes. https://arxiv.org/abs/2312.03238

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