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