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arXiv · 1512.02025

Large algebras of singular functions vanishing on prescribed sets

Luis Bernal-González·María del Carmen Calderón-Moreno
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Abstract

In this paper, the non-vacuousness of the family of all nowhere analytic infinitely differentiable functions on the real line vanishing on a prescribed set Z is characterized in terms of Z. In this case, large algebraic structures are found inside such family. The results obtained complete or extend a number of previous ones by several authors.

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Luis Bernal-González, María del Carmen Calderón-Moreno. 2015-12-07. Large algebras of singular functions vanishing on prescribed sets. https://arxiv.org/abs/1512.02025

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