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Results in Mathematics

, Volume 71, Issue 3–4, pp 1207–1221 | Cite as

Large Algebras of Singular Functions Vanishing on Prescribed Sets

  • Luis Bernal-González
  • María Del Carmen Calderón-MorenoEmail author
Article

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.

Mathematics Subject Classification

15A03 26B05 

Keywords

Nowhere analytic function lineability algebrability Pringsheim-singular function zero set 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Luis Bernal-González
    • 1
  • María Del Carmen Calderón-Moreno
    • 1
    Email author
  1. 1.Departamento de Análisis Matemático, Facultad de MatemáticasUniversidad de SevillaSevillaSpain

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