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.
This research project is concerned with the following three topics in approximation theory and Fourier analysis:
- 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.
- 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.
- 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.
- Yu. Kolomoitsev, T. Lomako, J. Prestin
On Lp-error of bivariate polynomial interpolation on the square
J. Approx. Theory 229 (2018), 13-35
- Yu. Kolomoitsev
On moduli of smoothness and averaged differences of fractional order
Fract. Calc. Appl. Anal. 20 (2017), no. 4, 988-1009
- Yu. Kolomoitsev, E. Liflyand
On weighted conditions for the absolute convergence of Fourier integrals
J. Math. Anal. Appl. 456 (2017), no. 1, 163-176
- Yu. Kolomoitsev
Best approximations and moduli of smoothness of functions and their derivatives in Lp, 0<p<1
- Yu. Kolomoitsev, M. Skopina
Approximation by multivariate Kantorovich-Kotelnikov operators
J. Math. Anal. Appl. 456 (2017), no. 1, 195-213
- Yu. Kolomoitsev, T. Lomako
Inequalities in approximation theory involving fractional smoothness in Lp, 0<p<1
- Yu. Kolomoitsev, S. Tikhonov
Hardy-Littlewood and Ulyanov inequalities
to appear in Mem. Amer. Math. Soc.
- Yu. Kolomoitsev, M. Skopina
Around Kotelnikov-Shannon formula
Conference: 2017 International Conference on Sampling Theory and Applications (SampTA), Tallin, Estonia, 2017, pp. 279-282
- Talk "Best approximations and moduli of smoothness of functions and their derivatives in Lp, 0<p<1", Institute of Mathematics NAS of Ukraine, Kiev, Ukraine, February 3, 2017.
- Talk "Best approximations and moduli of smoothness of functions and their derivatives in Lp, 0<p<1", Holon Institute of Technology, Holon, Israel , May 14, 2017.
- Talk "On the growth of Lebesgue constants for convex polyhedra", Bar-Ilan University, Ramat-Gan, Israel, May 15, 2017.
- Talk "Best approximations and moduli of smoothness of functions and their derivatives in Lp, 0<p<1", Technion - Israel Institute of Technology, Haifa, Israel, May 21, 2017.
- Talk "Approximation by multivariate Kantorovich-Kotelnikov sampling operators", Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, January 12, 2018.
- Talk "Approximation by generalized Kantorovich-Kotelnikov sampling operators", Seminari d'Anàlisi de Barcelona, March 05, 2018.
- New perspectives in the theory of function spaces and their applications (NPFSA-2017), Będlewo, Poland, September 17 - September 23, 2017.
- 6th Workshop on Fourier Analysis and Related Fields, Pécs, Hungary, August 24 - August 31, 2017.
- 11th International ISAAC Congress, Växjö, Sweden, August 14 - August 18, 2017
- Summer School in Lübeck "Modeling, Analysis, and Approximation Theory toward applications in tomography and inverse problems", Lübeck, Germany, July 31 - August 4, 2017.
- Foundations of Computational Mathematics (FoCM 2017) Barcelona, Spain, July 10 - July 19, 2017.
- Follow-up: Approximation Theory & Function Spaces, Barcelona, Spain, June 26 - June 30, 2017.
- Complex and Harmonic Analysis III, Holon and Haifa, Israel, June 04 - June 08, 2017.
- 3rd International Conference "Approximation Methods for Molecular Modelling and Diagnosis Tools", Kyiv, Ukraine, January 26 - January 30, 2017.
- Centre de Recerca Matemàtica, Barcelona, Spain, February 9 - March 2, 2017.
- Bar-Ilan University, Ramat-Gan, Israel, May 2 - June 18, 2017.
- Centre de Recerca Matemàtica, Barcelona, Spain, June 25 - July 13, 2017.
- Laboratoire d'Analyse et de Mathématiques Appliquées, University Paris-Est, Paris, France, October 14 - October 29, 2017.
- Centre de Recerca Matemàtica, Barcelona, Spain, February 28 - March 20, 2018.