Unconditionality of orthogonal spline systems in $L^p$

TL;DR

This paper proves that orthonormal spline systems of any order form an unconditional basis in reflexive L^p spaces for any dense point sequence.

Contribution

It establishes the unconditionality of orthogonal spline systems in L^p spaces for all orders and dense sequences, extending previous results.

Findings

Orthogonal spline systems are unconditional bases in reflexive L^p.

The result holds for any natural number order k.

The proof applies to any dense point sequence.

Abstract

Given any natural number $k$ and any dense point sequence $(t_n)$, we prove that the corresponding orthonormal spline system of order $k$ is an unconditional basis in reflexive $L^p$.