Maximal smoothness of the anti-analytic part of a trigonometric null series

On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness

In this paper, we give a characterization of Nikol'ski\uı-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to a such a class are given. In order to prove our results, we make use of certain recent reverse Copson- and Leindler-type inequalities.

Order estimates of the best orthogonal trigonometric approximations of classes of convolutions of periodic functions of not high smoothness

We obtain order estimates for the best uniform orthogonal trigonometric approximations of $2π$-periodic functions, whose $(ψ,β)$-derivatives belong to unit balls of spaces $L_{p}, \ 1\leq p<\infty$, in case at consequences $ψ(k)$ are that product $ψ(n)n^{\frac{1}{p}}$ can tend to zero slower than any power function and $\sum\limits_{k=1}^{\infty}ψ^{p'}(k)k^{p'-2}<\infty$ when $1<p<\infty$, $\frac{1}{p}+\frac{1}{p'}=1$ and $\sum\limits_{k=1}^{\infty}ψ(k)<\infty$ when $p=1$. We also establish the analogical estimates in $L_{s}$-metric, $1< s\leq \infty$, for classes of the summable $(ψ,β)$-diffe…

高光滑卷积类上插值三角多项式的逼近估计

Estimates of approximations by interpolation trigonometric polynomials on the classes of convolutions of high smoothness

该研究在高光滑周期卷积函数类上建立插值Lebesgue型不等式，用卷积核函数的最佳逼近估计插值三角多项式偏差，证明核序列快速衰减时不等式渐近精确并得到逐点逼近精确上界的渐近等式。