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Algebrability and nowhere Gevrey differentiability

Abstract

We show that there exist c-generated algebras (and dense in C ([0, 1])) every nonzero element of which is a nowhere Gevrey differentiable function. This leads to results of dense algebrability (and, therefore, lineability) of functions enjoying this property. In the process of proving these results we also provide a new construction of nowhere Gevrey differentiable functions.

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Correspondence to F. Bastin.

Additional information

The second author was supported by MTM2010-14909, and also wishes to thank Programa de Investigación y Desarrollo de la UPV, referencia SP20120700.

The third author was supported by a grant of Research Fellow from the Fonds National de la Recherche Scientifique (FNRS).

The fourth author was supported by CNPq Grant 401735/2013-3 (PVE — Linha 2).

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Cite this article

Bastin, F., Conejero, J.A., Esser, C. et al. Algebrability and nowhere Gevrey differentiability. Isr. J. Math. 205, 127–143 (2015). https://doi.org/10.1007/s11856-014-1104-1

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Keywords

  • American Mathematical Society
  • Topological Vector Space
  • Free Algebra
  • Separable Banach Space
  • Gevrey Class