arXiv subjects

M. Passenbrunner

Publications and source records attributed to M. Passenbrunner.

2 recordsLinked to original sources

arXiv2022

Multivariate orthogonal spline systems

In this article we consider orthonormal systems consisting of tensor products of splines. We show some convergence results of the corresponding orthogonal series including a.e. convergence and unconditional convergence in $L^p$ for $1<p<\infty$, where the latter is proved under some geometric conditions on the involved partitions that depend on the spline order.

math.CA↗

arXiv2017

Unconditionality of Periodic Orthonormal Spline Systems in $L^p$

Given any natural number $k$ and any dense point sequence $(t_n)$ on the torus $\mathbb T$, we prove that the corresponding periodic orthonormal spline system of order $k$ is an unconditional basis in $L^p$ for $1<p<\infty$.

math.FA↗