STECHKIN PROBLEM FOR A DIFFERENTIATION OPERATOR WITH ASYMMETRIC CONSTRAINTS

Nikita S. Payuchenko     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108, Russian Federation)

Abstract


The Landau–Kolmogorov inequality estimates the norm of an intermediate derivative by the product of the norms of the function and its highest-order derivative. The corresponding Stechkin problem concerns the best approximation of the differentiation operator by bounded linear operators. In this paper, we study the connection between Landau–Kolmogorov inequalities with asymmetric constraints on the highest-order derivative and the Stechkin problem. In analogy with existing works, in some cases we derive a naturally defined associated Stechkin problem and obtain the exact value of the problem and extremal operators. We employ methods similar to those used by S.B. Stechkin in his works on this topic.


Keywords


Stechkin problem, Landau–Kolmogorov inequality, Asymmetric constraints

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References


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DOI: http://dx.doi.org/10.15826/umj.2026.1.008

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