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Approximation of Poisson integrals by one linear approximation method in uniform and integral metrics
We obtain asymptotic equalities for the least upper bounds of approximations of classes of Poisson integrals of periodic functions by a linear approximation method of special form in the metrics ofExpand
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Order Estimates for the Best Approximations and Approximations by Fourier Sums in the Classes of Convolutions of Periodic Functions of Low Smoothness in the Uniform Metric
We obtain the exact-order estimates for the best uniform approximations and uniform approximations by Fourier sums in the classes of convolutions of periodic functions from the unit balls of theExpand
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Best Approximations and Widths of Classes of Convolutions of Periodic Functions of High Smoothness
We consider classes of 2π-periodic functions that are represented in terms of convolutions with fixed kernels Ψβ− whose Fourier coefficients tend to zero at exponential rate. We determine exactExpand
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On the existence and uniqueness of a solution of the problem of uniformSK-spline-interpolation
We establish necessary and sufficient conditions for the existence and uniqueness of generalized interpolatingSK-splines with a uniform distribution of interpolation points.
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Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials
We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the classes of periodic infinitely differentiable functions CβΨC whose elements can be represented inExpand
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On the best approximation of classes of convolutions of periodic functions by trigonometric polynomials
We present sufficient conditions for kernels to belong to the classNn*. In certain cases, this enables us to find exact values of the best approximations of classes of convolutions by trigonometricExpand
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Uniform approximation of Poisson integrals of functions from the class Hω by de la Vallée Poussin sums
We obtain asymptotic equalities for least upper bounds of deviations in the uniform metric of de la Vallée Poussin sums on the sets CβqHω of Poisson integrals of functions from the class Hω generatedExpand
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BY GENERALIZED ZYGMUND SUMS
We obtain asymptotic equalities for the least upper bounds of approximations by Zygmund sums in the uniform metric on the classes of continuous 2π-periodic functions whose (ψ, β)-derivatives belongExpand
Order estimation of the best approximations and of the approximations by Fourier sums of classes of $(\psi,\beta)$--diferentiable functions
There were established the exact-order estimations of the best uniform approximations by{\psi} the trigonometrical polynoms on the $C^{\psi}_{\beta,p}$ classes of $2\pi$-periodic continuous functionsExpand
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