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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The authors have been partially supported by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 Grant P08-FQM-03543 and by MEC Grant MTM2015-65242-C2-1-P.
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Bernal-González, L., Calderón-Moreno, M.D.C. Large Algebras of Singular Functions Vanishing on Prescribed Sets. Results Math 71, 1207–1221 (2017). https://doi.org/10.1007/s00025-016-0569-0
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DOI: https://doi.org/10.1007/s00025-016-0569-0