Differentiability of the functions of the generalized Takagi Class

Abstract

We introduce a generalization of the Takagi Class, considering an arbitrary countable dense set instead of the dyadic numbers that appear in the original Takagi function. This generalization contains many of the previous generalizations. We study the differentiation of the functions belonging to this Class, as well as the measure of the set of points of differentiability characterizing them through properties of the weights sequence. Finally, we prove that the Class is a Banach space isometric to $$\ell ^1$$.