Approximations of entire functions by polynomials of the best standard approximation
We find asymptotic equality for the top limits of approaching by the polynomials of best mean approximation on classes of $2\pi$--periodic functions $C^\psi_{\overline\beta,s}$, $1\leq s \leq\infty$, and $C^\psi_{\overline\beta}H_\omega$, that are set by multipliers $\psi(k)$ and by shifts forward a...
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| Datum: | 2017 |
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| Ключові слова: | keywords |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Інститут математики НАН України
2017
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| Online Zugang: | https://trim.imath.kiev.ua/index.php/trim/article/view/105 |
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| Назва журналу: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Zusammenfassung: | We find asymptotic equality for the top limits of approaching by the polynomials of best mean approximation on classes of $2\pi$--periodic functions $C^\psi_{\overline\beta,s}$, $1\leq s \leq\infty$, and $C^\psi_{\overline\beta}H_\omega$, that are set by multipliers $\psi(k)$ and by shifts forward an argument $\beta_k$ on condition that sequences $\psi(k)$ fall to the zero more quickly, than any geometrical progression (in this case functions from the noted classes assume regular extension upon the whole complex plane). |
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