Unconditionality of orthogonal spline systems in $H^1$

TL;DR

This paper characterizes the knot sequences that make orthonormal spline systems of any order an unconditional basis in the Hardy space H^1, providing a geometric criterion.

Contribution

It offers a simple geometric characterization of knot sequences ensuring unconditionality of spline systems in H^1, advancing understanding of basis properties in Hardy spaces.

Findings

Identifies geometric conditions for knot sequences

Establishes unconditional basis property in H^1

Applies to spline systems of arbitrary order

Abstract

We give a simple geometric characterization of knot sequences for which the corresponding orthonormal spline system of arbitrary order $k$ is an unconditional basis in the atomic Hardy space $H^1[0,1]$.