dc.contributor.author | Avetisyan, Z | |
dc.contributor.author | Grigoryan, M | |
dc.contributor.author | Ruzhansky, M | |
dc.date.accessioned | 2020-11-17T11:24:48Z | |
dc.date.available | 2020-11-03 | |
dc.date.available | 2020-11-17T11:24:48Z | |
dc.date.issued | 2020 | |
dc.identifier.issn | 0025-5874 | |
dc.identifier.uri | https://qmro.qmul.ac.uk/xmlui/handle/123456789/68368 | |
dc.description.abstract | For a separable finite diffuse measure space $\mathcal{M}$ and an orthonormal basis $\{\varphi_n\}$ of $L^2(\mathcal{M})$ consisting of bounded functions $\varphi_n\in L^\infty(\mathcal{M})$, we find a measurable subset $E\subset\mathcal{M}$ of arbitrarily small complement $|\mathcal{M}\setminus E|<\epsilon$, such that every measurable function $f\in L^1(\mathcal{M})$ has an approximant $g\in L^1(\mathcal{M})$ with $g=f$ on $E$ and the Fourier series of $g$ converges to $g$, and a few further properties. The subset $E$ is universal in the sense that it does not depend on the function $f$ to be approximated. Further in the paper this result is adapted to the case of $\mathcal{M}=G/H$ being a homogeneous space of an infinite compact second countable Hausdorff group. As a useful illustration the case of $n$-spheres with spherical harmonics is discussed. The construction of the subset $E$ and approximant $g$ is sketched briefly at the end of the paper. | en_US |
dc.publisher | Springer (part of Springer Nature) | en_US |
dc.relation.ispartof | Mathematische Zeitschrift | |
dc.rights | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | |
dc.subject | math.FA | en_US |
dc.subject | math.FA | en_US |
dc.subject | 41A99, 43A15, 43A50, 43A85, 46E30 | en_US |
dc.title | Approximations in $L^1$ with convergent Fourier series | en_US |
dc.type | Article | en_US |
dc.rights.holder | © 2020, The Author(s) | |
pubs.author-url | http://arxiv.org/abs/1810.06047v1 | en_US |
pubs.notes | Not known | en_US |
pubs.publication-status | Accepted | en_US |
dcterms.dateAccepted | 2020-11-03 | |
rioxxterms.funder | Default funder | en_US |
rioxxterms.identifier.project | Default project | en_US |