The Lebesgue Constant for the Periodic Franklin System

We identify the torus with the unit interval $[0,1)$ and let $n,\nu \in \mathbb{N}$, $1\le \nu \le n-1$ and $N:=n+\nu$. Then we define the (partially equally spaced) knots $$t_j=\{[c]ll$$ This shows in particular that the Lebesgue constant of the classical Franklin orthonormal system on the torus is $2+\frac{33-18\sqrt{3}}{13}$.