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

Abstract

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 \(H^{1}(\mathbb{T})\).