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A sharp Remez inequality for trigonometric polynomialsстатья
- Авторы: Nursultanov E.D., Tikhonov S.
- Журнал: Centre de Reserca Matematica, Prenrints
- Том: 1045
- Год издания: 2011
- Первая страница: 1
- Последняя страница: 20
- Аннотация: We obtain a sharp Remez inequality for the trigonometric polynomial T n of degree n on [0,2π): ∥Tn∥L∞([0,2π))≤(1+2tan2nβ4m)∥Tn∥L∞([0,2π)∖B), where 2πm is the minimal period of T n and |B|=β<2πmn is a measurable subset of T . In particular, this gives the asymptotics of the sharp constant in the Remez inequality: for a fixed n, C(n,β)=1+(nβ)28+O(β4),β→0, where C(n,β):=sup|B|=βsupTn∥Tn∥L∞([0,2π))∥Tn∥L∞([0,2π)∖B). We also obtain sharp Nikol’skii’s inequalities for the Lorentz spaces and net spaces. Multidimensional variants of Remez and Nikol’skii’s inequalities are investigated.
- Добавил в систему: Нурсултанов Ерлан Даутбекович