On the Lebesgue constants
UDC 517.5 We give the solution of a classical problem of approximation theory on sharp asymptotic of the Lebesgue constants or norms of the Fourier – Laplace projections on the real spheres $\mathbb{S}^{d},$ complex $\mathrm{P}^{d}(\mathbb{C})$ and quaternionic $\mathrm{P}^{d}(\mathbb{H})$ proje...
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| Datum: | 2019 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2019
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1499 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.5
We give the solution of a classical problem of approximation theory on sharp asymptotic of the Lebesgue constants or
norms of the Fourier – Laplace projections on the real spheres $\mathbb{S}^{d},$ complex $\mathrm{P}^{d}(\mathbb{C})$ and quaternionic
$\mathrm{P}^{d}(\mathbb{H})$ projective spaces, and the Cayley elliptic plane $\mathrm{P}^{16}(\mathrm{Cay}).$ In particular, these results extend sharp asymptotic found by Fejer in the
case of $\mathbb{S}^{1}$ in 1910 and by Gronwall in 1914 in the case of $\mathbb{S}^{2}$ . |
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