2019
Том 71
№ 11

All Issues

Telyakovskii S. A.

Articles: 4
Article (Russian)

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

Telyakovskii S. A.

↓ Abstract   |   Full text (.pdf)

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

Subbotin Yu. N., Telyakovskii S. A.

↓ Abstract   |   Full text (.pdf)

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

Telyakovskii S. A.

↓ Abstract   |   Full text (.pdf)

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

Telyakovskii S. A.

Full text (.pdf)

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