On correlation between sharp Kolmogorov type inequalities and sharp Kolmogorov–Remez type inequalities
Abstract
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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