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Uniform Convergence of Trigonometric Series with Rarely Changing Coefficients

- S. A. Telyakovskiĭ
- Mathematics
- 1 September 2001

AbstractWe consider the series
$$\sum\nolimits_{k = 1}^\infty {a_k \sin kx}$$
and
$$\frac{{a_0 }}{2} + \sum\nolimits_{k = 1}^\infty {a_k \cos kx}$$
whose coefficients satisfy the condition
$$a_k… Expand

Concerning a sufficient condition of sidon for the integrability of trigonometric series

- S. A. Telyakovskiĭ
- Mathematics
- 1 September 1973

AbstractWe consider problems concerning integrability and convergence in the metric L of trigonometric series, the coefficientsak of which satisfy the conditions:ak → 0, there exist numbers Ak such… Expand

Approximation of functions of higher smoothness by Fourier sums

- S. A. Telyakovskiĭ
- Mathematics
- 1 April 1989

Approximation by Bernstein polynomials at the points of discontinuity of the derivatives

- S. A. Telyakovskiĭ
- Mathematics
- 7 May 2009

It is proved that, in the asymptotic formulas for the deviations of Bernstein polynomials from functions at the points of discontinuity of the first kind of the highest even-order derivative, the… Expand

Lower bounds of the integral modulus of continuity of a function in terms of its Fourier coefficients

- S. A. Telyakovskiĭ
- Mathematics
- 1 November 1992

Estimating the integral of the derivative of the sum of a trigonometric series with quasi-convex coefficients

- S. A. Telyakovskiĭ
- Mathematics
- 31 December 1995

For the sum of series in sines or in cosines with quasi-convex coefficients, representation of their first derivatives are found in terms of the second differences of the sequence of coefficients of… Expand

Exact values of relative widths of classes of differentialbe functions

- Yu. N. Subbotin, S. A. Telyakovskiĭ
- Mathematics
- 1 June 1999

AbstractWe study relative widths in the spacesC andL of classes of periodic differentiable functionsWr,r=1,2,…, when in contrast to the Kolmogorov widths it is additionally required that the… Expand

COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: Relative widths of classes of differentiable functions in the L2 metric

- Yu. N. Subbotin, S. A. Telyakovskiĭ
- Mathematics
- 31 August 2001

On the equality of Kolmogorov and relative widths of classes of differentiable functions

- Yu. N. Subbotin, S. A. Telyakovskiĭ
- Mathematics
- 10 November 2009

We obtain sharper estimates of the remainders in the expression for the least value of the multiplier M for which the Kolmogorov widths dn(WCr, C) and the relative widths Kn (WCr,MWCj,C) of the class… Expand

Sharpening of the estimates for relative widths of classes of differentiable functions

- Yu. N. Subbotin, S. A. Telyakovskiĭ
- Mathematics
- 9 September 2010

We improve the earlier obtained upper estimates for the least value of the coefficient M for which the Kolmogorov widths dn(WCr, C) of the function class WCr are equal to the relative widths Kn(WCr,… Expand

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