On properties of functions in exponential Takagi class

The structure of functions in exponential Takagi class are similar to the Takagi continuous nowhere differentiable function described in 1903. These functions have one real parameter $v$ and are defined by the series $T_v(x)=\sum_{n=0}^\infty v^nT_0(2^nx)$, where $T_0(x)$ is the distance from $x\in\mathbb R$ to the nearest integer. For various values of $v$, we study the domain of such functions, their continuity, Hölder property, differentiability and concavity. Providing known results and proving missing facts, we give the complete description of these properties for each value of parameter $v$.