On the sets of divergence of multiple Fourier–Haar series
UDC 517.518.45 It is shown that every at most countable set $F$ in an $n$-dimensional unit cube $[0,1]^n$ is a set of divergence of the $n$-fold Fourier–Haar series of a certain limited dimensional function, i.e., there exists a bounded dimensional function defined on $[0,1]^n$ whose $n$-fold Fourie...
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| Datum: | 2023 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/6886 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.518.45
It is shown that every at most countable set $F$ in an $n$-dimensional unit cube $[0,1]^n$ is a set of divergence of the $n$-fold Fourier–Haar series of a certain limited dimensional function, i.e., there exists a bounded dimensional function defined on $[0,1]^n$ whose $n$-fold Fourier–Haar series converges in Pringsheim's sense on $[0,1]^n\backslash F$ and diverges on the cubes on $F.$ |
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| DOI: | 10.37863/umzh.v74i12.6886 |