Properties of local orthonormal systems, Part III: Variation spaces
Functional Analysis
2024-02-23 v2
Abstract
In [Y.~K.~Hu, K.~A.~Kopotun, X.~M.~Yu, Constr. Approx. 2000], the authors have obtained a characterization of best -term piecewise polynomial approximation spaces as real interpolation spaces between and some spaces of bounded dyadic ring variation. We extend this characterization to the general setting of binary filtrations and finite-dimensional subspaces of as discussed in our earlier papers [J.~Gulgowski, A.~Kamont, M.~Passenbrunner, arXiv:2303.16470 and arXiv:2304.05647]. Furthermore, we study some analytical properties of thus obtained abstract spaces of bounded ring variation, as well as their connection to greedy approximation by corresponding local orthonormal systems.
Keywords
Cite
@article{arxiv.2310.17309,
title = {Properties of local orthonormal systems, Part III: Variation spaces},
author = {Jacek Gulgowski and Anna Kamont and Markus Passenbrunner},
journal= {arXiv preprint arXiv:2310.17309},
year = {2024}
}