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arXiv · 2310.17309

Properties of local orthonormal systems, Part III: Variation spaces

Jacek Gulgowski·Anna Kamont·Markus Passenbrunner
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Abstract

In [Y.~K.~Hu, K.~A.~Kopotun, X.~M.~Yu, Constr. Approx. 2000], the authors have obtained a characterization of best $n$-term piecewise polynomial approximation spaces as real interpolation spaces between $L^p$ and some spaces of bounded dyadic ring variation. We extend this characterization to the general setting of binary filtrations and finite-dimensional subspaces of $L^\infty$ 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.

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Jacek Gulgowski, Anna Kamont, Markus Passenbrunner. 2023-10-26. Properties of local orthonormal systems, Part III: Variation spaces. https://arxiv.org/abs/2310.17309

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