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On the Relationship between Sharp Kolmogorov-Type Inequalities and Sharp Kolmogorov–Remez-Type Inequalities

Ukrainian Mathematical Journal, 2021
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Strengthening of Kolmogorov Type Inequalities for Derivatives and Differences

Journal of Mathematical Sciences, 2019
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On Kolmogorov-type inequalities for functions defined on a semiaxis

Ukrainian Mathematical Journal, 2007
Summary: We established necessary and sufficient conditions for the existence of a function from the class \(S^-\) with given integral norms of three successive derivatives (generally speaking, of fractional order).
Babenko, V. F., Skorokhodov, D. S.
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Multivariate Inequalities of Kolmogorov Type and Their Applications

1997
Connections of inequalities of Kolmogorov type given in the form of inequalities for support functions of convex sets with some problems of analysis will be investigated. Our results will be oriented to applications in multivariate approximation. Exact inequalities which estimate L2-norms of derivatives of a multivariate periodic function with the help
V. F. Babenko   +2 more
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Discrete and shift Kolmogorov type inequalities

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1983
SynopsisThe operators Δhf ≡ f(x) on function spaces and Δxn ≡ xn+1–xn on sequence spaces replace derivatives to yield analogues of the Kolmogorov inequality. Estimates for best constants are given for many spaces and for a few the best constants are actually given.
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Multivariate Landau–Kolmogorov-type inequality

Mathematical Proceedings of the Cambridge Philosophical Society, 1989
AbstractAssuming that the nth iterate of the Laplacian Δnf belongs to L∞(ℝ), we show for 0 < k < 2n thatwhere ∂/∂ξi is the derivative in the ei direction. The result is also extended to other Banach spaces of functions on ℝd.
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Kolmogorov-type inequalities and the best formulas for numerical differentiation

Mathematical Notes of the Academy of Sciences of the USSR, 1968
For a certain class of complex-valued functionsf(x), −∞
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Kolmogorov-Type Inequalities for Fractional Derivatives on the Half Line

Ukrainian Mathematical Journal, 2014
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On an inequality of the Kolmogorov type for a second-order differential expression

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1993
Abstract In this paper we discuss an integro-differential inequality formed from the square of a second-order differential expression. A connection between the existence of the inequality and the Titchmarsh–Weyl m-function is established and it is shown that the best constant in the inequality is determined by the behaviour of the m ...
Beynon, M. J.   +2 more
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On the connection between certain inequalities of the Kolmogorov type for periodic and nonperiodic functions

Ukrainian Mathematical Journal, 1999
Summary: Nonperiodic analogs are obtained of the known inequalities which estimate \(L_{p}\)-norms of intermediate derivatives of a periodic function in terms of \(L_{\infty}\)-norms and the higher derivative of the considered function.
Babenko, V. F., Selivanova, S. A.
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