• Yurii Kolomoitsev
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  • Project - AFFMA
  • Approximation of Functions and Fourier Multipliers and their applications - AFFMA

    1 November 2016 — 31 October 2018

    This project has received funding from the European Union's Horizon 2020 research and innovation programm under the Marie Skłodowska-Curie grant agreement No 704030.

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    Objective:

    This research project is concerned with the following three topics in approximation theory and Fourier analysis:
    1. Simultaneous approximation of functions and their derivatives in Lp, 0<p<1. We expect to investigate classes of functions and different methods of approximation for which the problem of simultaneous approximation is solvable, and to obtain estimates for the errors of the best approximation of functions and their derivatives for particular methods of approximation in Lp, 0<p<1.
    2. New inequalities for moduli of smoothness of functions in Lp, 0<p<1. We expect to find the classes of functions for which the direct and inverse inequalities for moduli of smoothness of functions and their derivatives hold, and to investigate the sharp Ulyanov inequality for different concepts of smoothness.
    3. Fourier multipliers and families of multiplier operators in Lp, p>0. We expect to obtain sufficient conditions of the boundedness for such operators in terms of the simultaneous behavior of a multiplier and its derivatives in different functional spaces, and to apply such conditions for solving problems from this proposal.

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