Unconditionality of Periodic Orthonormal Spline Systems in \(\boldsymbol{H}^{\mathbf{1}}{(\mathbb{T})}\): Necessity

We give a geometric characterization of knot sequences \((s_{n})\) , which is a necessary condition for the corresponding periodic orthonormal spline system of arbitrary order \(k\) , \(k\in\mathbb{N}\) , to be an unconditional basis in the atomic Hardy space on the torus \(H^{1}(\mathbb{T})\) .