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