Properties of local orthonormal systems, Part III: Variation spaces
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911781788581888 |
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| author | Gulgowski, Jacek Kamont, Anna Passenbrunner, Markus |
| author_facet | Gulgowski, Jacek Kamont, Anna Passenbrunner, Markus |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_17309 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Properties of local orthonormal systems, Part III: Variation spaces Gulgowski, Jacek Kamont, Anna Passenbrunner, Markus Functional Analysis 41A46, 26A45, 42C05, 42C40, 46E30 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. |
| title | Properties of local orthonormal systems, Part III: Variation spaces |
| topic | Functional Analysis 41A46, 26A45, 42C05, 42C40, 46E30 |
| url | https://arxiv.org/abs/2310.17309 |