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AFFMA

Approximation of Functions and Fourier Multipliers and their applications

Total Cost €

EC-Contrib. €

Partnership

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Outcomes and
results

AFFMA project word cloud

Explore the words cloud of the AFFMA project. It provides you a very rough idea of what is the project "AFFMA" about.

obtain inequality tools 0 society teams simultaneously concerning intersectoral multiplier lt spaces gt boundedness skills ukrainian universal powerful smoothness solvable solving sharp estimates ulyanov qualified concerned direct fourier multipliers operators lp errors questions researcher lasting simultaneous functions training families competence approximation inverse inequalities cooperation moduli contrary newly p classes functional theory international sufficient combine behavior specialists mobility derivatives acquisition hold mentioned

Project "AFFMA" data sheet

The following table provides information about the project.

Coordinator	UNIVERSITAET zu LUEBECK Organization address address: RATZEBURGER ALLEE 160 city: LUBECK postcode: 23562 website: http://www.uni-luebeck.de/ 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	http://www.math.uni-luebeck.de/mitarbeiter/kolomoitsev/affma.php
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

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	UNIVERSITAET zu LUEBECK UNIVERSITAET zu LUEBECK Organization address address: RATZEBURGER ALLEE 160 city: LUBECK postcode: 23562 website: http://www.uni-luebeck.de/ contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	DE (LUBECK)	coordinator	171˙460.00

Map

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.

Publications

List of publications.
year	authors and title	journal	last update
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, JÃ¼rgen 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 Kantorovichâ€“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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