2019
Том 71
№ 11

# Telyakovskii S. A.

Articles: 4
Article (Russian)

### On the properties of blocks of terms of the series $\sum \cfrac1k \sin kx$

Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 713-718

We investigate the decomposability of the series $\sum \cfrac1k \sin kx$ into blocks such that the sum of the series formed of the moduli of these blocks belongs to the spaces $L^p[0, \pi]$ or the spaces $L^p[0, \pi]$ with weight $x^{-\gamma},\quad \gamma < 1$.

Article (Russian)

### On relative widths of classes of differentiable functions. II

Ukr. Mat. Zh. - 2010. - 62, № 3. - pp. 423–431

We obtain an upper bound for the least value of the factor $М$ for which the Kolmogorov widths $d_n (W_C^r, C)$ are equal to the relative widths $K_n (W^C_r, MW^C_j, C)$ of the class of functions $W_C^r$ with respect to the class $MW^C_j$, provided that $j > r$. This estimate is also true in the case where the space $L$ is considered instead of $C$.

Article (Russian)

### Estimation of the moduli of continuity of one-variable functions in the metric of $L$ in terms of fourier coefficients

Ukr. Mat. Zh. - 1994. - 46, № 5. - pp. 626–632

This paper is a survey of results concerning the estimation of the moduli of continuity of functions in the metric of L in terms of their Fourier coefficients. Upper bounds, lower bounds, and asymptotic estimates of the moduli of continuity are presented.

Article (Russian)

### Approximation of functions satisfying Lipschitz conditions by Féjer sums

Ukr. Mat. Zh. - 1969. - 21, № 3. - pp. 334–343