Scientific heritage of Ukrainian mathematician V. K. Dzyadyk (to the centennial of the birth)

Petro V. Zaderei, Nadiya M. Zaderei, Galyna D. Nefodova

Abstract


18th February 2019 is the centennial of the birth of renowned Ukrainian mathematician, corresponding member of NAS, V. K. Dzyadyk, whose scientific heritage has important results for functions approximation theory. The scientist‘s major works are related to constructive complex variable theory. The paper covers two important problems the solutions of which led the scientist to worldwide fame. These are Favard problem of best approximation of class ${{W}^{r}}$ functions with fractionary $r$ and Kolmogorov–Nikolsky problem on precise suprema of deviations of Fourier series linear methods summation for some classes ${{W}^{r}}{{H}_{\omega }}.$
V. K. Dzyadyk made a considerable contribution to the development of approximation theory and combined fruitful scientifi c work with brilliant pedagogical activity.

Keywords


Favard problem; Kolmogorov–Nikolsky problem; Approximation theory; Best approximation; Favard constants; Fourier series linear methods summation; Fejér sums; Rogozinski method

References


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