The functions $f$ and $g$ are defined for all non-integral values and are continuous there.

Both $f$ and $g$ are periodic of period $1$, that is $f(x+1)=f(x)$ and $g(x+1)=g(x)$ hold for all $x\in \mathbb{R}\setminus \mathbb{Z}$.

Both $f$ and $g$ are odd functions, that is we have $f(-x)=-f(x)$ and $g(-x)=-g(x)$ for all $x\in \mathbb{R}\setminus \mathbb{Z}$.

The two functions $f$ and $g$ satisfy the same functional equation: $f(\frac{x}{2})+f(\frac{x+1}{2})=2f(x)$ and $g(\frac{x}{2})+g(\frac{x+1}{2})=gf(x)$.

By setting $h(x):=0$ for $x\in \mathbb{Z}$, $h$ becomes a continuous function on all of $\mathbb{R}$ that shares the properties given in 26.2, 26.3, 26.4.