Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line

In this paper we establish some new Kolmogorov type inequalities for the Marchaud and Hadamard fractional derivatives of functions defined on a real axis or semi-axis. Simultaneously we solve two related problems: the Stechkin problem on the best approximation of unbounded operators by bounded ones...

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Bibliographic Details
Main Authors Babenko, V. F, Churilova, M. S, Parfinovych, N. V, Skorokhodov, D. S
Format Journal Article
LanguageEnglish
Published 28.10.2014
Subjects
Mathematics - Functional Analysis
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Summary:In this paper we establish some new Kolmogorov type inequalities for the Marchaud and Hadamard fractional derivatives of functions defined on a real axis or semi-axis. Simultaneously we solve two related problems: the Stechkin problem on the best approximation of unbounded operators by bounded ones on a given class of elements and the problem of optimal recovery of operator on elements from some class given with prescribed error. Keywords: inequalities for derivatives, fractional derivatives, approx- imation of unbounded operators by bounded ones, optimal recovery of operators, ideal lattice.
DOI:10.48550/arxiv.1410.7829