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Approximation of Functions and Fourier Multipliers and their applications

Total Cost €


EC-Contrib. €






Project "AFFMA" data sheet

The following table provides information about the project.


Organization address
city: LUBECK
postcode: 23562

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Germany [DE]
 Project website
 Total cost 171˙460 €
 EC max contribution 171˙460 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2015
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2016
 Duration (year-month-day) from 2016-11-01   to  2018-10-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITAET zu LUEBECK DE (LUBECK) coordinator 171˙460.00


 Project 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.

In our approaches we will combine the methods from approximation theory and Fourier analysis simultaneously, contrary to the previous research concerning the mentioned tasks. Moreover, by using and developing the newly introduced concepts of families of multiplier operators in Lp, 0<p<1, we will provide powerful and universal tools for solving the problems of this proposal as well as for further analysis of operators and related questions in the spaces Lp, 0<p<1.

Working on the proposed research tasks in the teams of very qualified specialists will allow the experienced researcher to enhance his competence in terms of skills acquisition through advanced training, international and intersectoral mobility, to develop a long-lasting research cooperation and to increase the impact of his future activities on European and Ukrainian society.


year authors and title journal last update
List of publications.
2017 Yurii Kolomoitsev
On moduli of smoothness and averaged differences of fractional order
published pages: , ISSN: 1311-0454, DOI: 10.1515/fca-2017-0051
Fractional Calculus and Applied Analysis 20/4 2019-06-13
2018 Yurii Kolomoitsev
Best approximations and moduli of smoothness of functions and their derivatives in L p , 0 < p < 1
published pages: 12-42, ISSN: 0021-9045, DOI: 10.1016/j.jat.2018.04.012
Journal of Approximation Theory 232 2019-06-13
2017 Yu. Kolomoitsev, E. Liflyand
On weighted conditions for the absolute convergence of Fourier integrals
published pages: 163-176, ISSN: 0022-247X, DOI: 10.1016/j.jmaa.2017.06.083
Journal of Mathematical Analysis and Applications 456/1 2019-06-13
2018 Yurii Kolomoitsev, Tetiana Lomako, Jürgen Prestin
On L p -error of bivariate polynomial interpolation on the square
published pages: 13-35, ISSN: 0021-9045, DOI: 10.1016/j.jat.2018.02.005
Journal of Approximation Theory 229 2019-06-13
2017 Yu. Kolomoitsev, M. Skopina
Approximation by multivariate Kantorovich–Kotelnikov operators
published pages: 195-213, ISSN: 0022-247X, DOI: 10.1016/j.jmaa.2017.06.081
Journal of Mathematical Analysis and Applications 456/1 2019-06-13

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