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arXiv · 1410.7829

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

V. F. Babenko·M. S. Churilova·N. V. Parfinovych·D. S. Skorokhodov
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Abstract

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.

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V. F. Babenko, M. S. Churilova, N. V. Parfinovych, D. S. Skorokhodov. 2014-10-28. Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line. https://arxiv.org/abs/1410.7829

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