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Best approximation of the differentiation operator on the class of functions analytic in a strip

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Abstract

On the class of functions analytic in a strip, we study a number of related extremal problems for the differentiation operator: the best approximation of the operator, computation of its modulus of continuity, and optimal recovery of the operator from boundary values of a function given with error on a straight line.

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References

  1. R. R. Akopyan, “Best approximation of the operator of analytic continuation on the class of functions analytic in a strip,” Trudy Inst. Mat. Mekh. UrO RAN 17(3), 46–54 (2011).

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  2. V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems,” Russ. Math. Surv. 51(6), 1093–1126 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  3. S. B. Stechkin, “Inequalities between the norms of derivatives of an arbitrary function,” Acta Sci. Math. 26(3–4), 225–230 (1965).

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  4. S. B. Stechkin, “Best approximation of linear operators,” Math. Notes 1(2), 91–99 (1967).

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  5. K. Yu. Osipenko, Optimal Recovery of Analytic Functions (Nova Science, Huntington, NY, 2000).

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Authors and Affiliations

  1. Ozersk Institute of Technology, National Research Nuclear University MEPhI, pr. Pobedy 48, Ozersk, 456783, Russia

    R. R. Akopyan

  2. Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina 51, Yekaterinburg, 620000, Russia

    R. R. Akopyan

Authors
  1. R. R. Akopyan
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Correspondence to R. R. Akopyan.

Additional information

Original Russian Text © R.R. Akopyan, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 1.

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Akopyan, R.R. Best approximation of the differentiation operator on the class of functions analytic in a strip. Proc. Steklov Inst. Math. 288 (Suppl 1), 5–12 (2015). https://doi.org/10.1134/S0081543815020029

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  • DOI: https://doi.org/10.1134/S0081543815020029

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