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On reconstruction of multiplicative transformations of functions in anisotropic spaces

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Abstract

We construct a reconstruction operator for multiplicative transformations of functions in anisotropic spaces from their values at a given number of points. We show that the error of the reconstruction of a function in W α p coincides in order with the corresponding orthodiameter.

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Authors and Affiliations

  1. Kazakhstan Branch of Lomonosov Moscow State University Eurasian National University, Astana, Kazakhstan

    E. D. Nursultanov & N. T. Tleukhanova

Authors
  1. E. D. Nursultanov
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  2. N. T. Tleukhanova
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Correspondence to E. D. Nursultanov.

Additional information

Original Russian Text Copyright © 2014 Nursultanov E.D. and Tleukhanova N.T.

The authors were financially supported by the Committee of Science of the Republic of Kazakhstan (Grants 1412/GF, 0744/GF, and 1504/GF).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 3, pp. 592–609, May–June, 2014.

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Nursultanov, E.D., Tleukhanova, N.T. On reconstruction of multiplicative transformations of functions in anisotropic spaces. Sib Math J 55, 482–497 (2014). https://doi.org/10.1134/S0037446614030100

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  • DOI: https://doi.org/10.1134/S0037446614030100

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