On correlation between sharp Kolmogorov type inequalities and sharp Kolmogorov–Remez type inequalities
UDC 517.5 We establish a new theorem on correlation between the sharp constants in the Kolmogorov type inequalities and the sharp constants in the Kolmogorov–Remez type inequalities for differentiable periodic functions. As a consequence, we obtain new sharp Kolmogorov–Remez type inequalities for s...
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| Datum: | 2021 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/6310 |
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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 establish a new theorem on correlation between the sharp constants in the Kolmogorov type inequalities and the sharp constants in the Kolmogorov–Remez type inequalities for differentiable periodic functions. As a consequence, we obtain new sharp Kolmogorov–Remez type inequalities for such functions. We also derive new sharp Bernstein–Remez type inequalities for trigonometric polynomials and polynomial splines.
 
 
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| DOI: | 10.37863/umzh.v73i4.6310 |