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dc.contributor.authorFernández, E.
dc.contributor.authorRoncal, L.
dc.date.accessioned2019-08-12T13:21:46Z
dc.date.available2019-08-12T13:21:46Z
dc.date.issued2019-03-22
dc.identifier.issn0010-1354
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1004
dc.description.abstractIn this note we present some simple counterexamples, based on quadratic forms in infinitely many variables, showing that the implication $f\in C^{(\infty}(\mathbb{T}^\omega)\Longrightarrow\sum_{\bar{p}\in\mathbb{Z}^\infty}|\widehat{f}(\bar{p})|<\infty$ is false. There are functions of the class $C^{(\infty}(\mathbb{T}^\omega)$ (depending on an infinite number of variables) whose Fourier series diverges absolutely. This fact establishes a significant difference to what happens in the finite dimensional case.en_US
dc.description.sponsorshipBCAM Severo Ochoa excellence accreditation SEV-2013-0323 MTM2015-65888-C04-4-P 2017 Leonardo grant for Researchers and Cultural Creators, BBVA Foundationen_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectInfinite dimensional torusen_US
dc.subjectFourier seriesen_US
dc.subjectabsolute divergenceen_US
dc.subjectquadratic formsen_US
dc.titleOn the absolute divergence of Fourier series in the infinite dimensional torusen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.relation.publisherversionhttps://www.impan.pl/en/publishing-house/journals-and-series/colloquium-mathematicum/all/157/1/112945/on-the-absolute-divergence-of-fourier-series-on-the-infinite-dimensional-torusen_US
dc.relation.projectIDES/1PE/MTM2017-82160-C2-1-Pen_US
dc.relation.projectIDEUS/BERC/BERC.2018-2021en_US
dc.rights.accessRightsinfo:eu-repo/semantics/embargoedAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersionen_US
dc.journal.titleColloquium Mathematicumen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España