${\ell }^1$-summability and Fourier series of B-splines with respect to their knots

Martin Buhmann, Janin Jäger, Yuan Xu

We study the ${\ell }^1$-summability of functions in the $d$-dimensional torus ${\mathbb{T}}^d$ and so-called ${\ell }^1$-invariant functions. Those are functions on the torus whose Fourie…