# Algebrability and nowhere Gevrey differentiability

Autores UPV Conejero Casares, José Alberto 2015 ISRAEL JOURNAL OF MATHEMATICS

## Abstract

We show that there exist c-generated algebras (and dense in $C^\infty([0, 1]))$ 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 func- tions.