Large algebras of singular functions vanishing on prescribed sets
classification
🧮 math.FA
keywords
familyfunctionslargeprescribedvanishingalgebraicalgebrasanalytic
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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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