Publications
Article · Sbornik Mathematics · April 16, 2019
Smoothness of functions and Fourier coefficients
Mikhail Ivanovich Dyachenko, Askhat Birlesovich Mukanov, Sergey Yu. Tikhonov
Abstract
Abstract We consider functions represented as trigonometric series with general monotone Fourier coefficients. The main result of the paper is the equivalence of the modulus of smoothness, , of such functions to certain sums of their Fourier coefficients. As applications, for such functions we give a description of the norm in the Besov space and sharp direct and inverse theorems in approximation theory. Bibliography: 34 titles.
Approximation Theory and Sequence SpacesAdvanced Harmonic Analysis ResearchMathematical Approximation and Integrationmodulus of smoothnesstrigonometric seriesFourier coefficients
More by Askhat Mukanov
- On $$L_p$$-Integrability of Functions with General Monotone Fourier CoefficientsJournal of Fourier Analysis and Applications · 2026
- LORENTZ-TYPE THEOREMS IN LIPSCHITZ CLASSESScientific works/Elmi eserler · 2026
- Lorentz-type theorems for the Fourier transformsRendiconti del Circolo Matematico di Palermo Series 2 · 2026
- On $$L_p$$-Integrability of Multiple Trigonometric Series with General Monotone CoefficientsProceedings of the Steklov Institute of Mathematics · 2025 · Citations: 1