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Uniform Convergence of Trigonometric Series with Rarely Changing Coefficients
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_kExpand
Concerning a sufficient condition of sidon for the integrability of trigonometric series
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 suchExpand
Approximation by Bernstein polynomials at the points of discontinuity of the derivatives
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, theExpand
Estimating the integral of the derivative of the sum of a trigonometric series with quasi-convex coefficients
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 ofExpand
Exact values of relative widths of classes of differentialbe functions
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 theExpand
On the equality of Kolmogorov and relative widths of classes of differentiable functions
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 classExpand
Sharpening of the estimates for relative widths of classes of differentiable functions
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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