相关论文: Approximation by Fourier sums on the classes of ge…
We find asymptotic equalities for exact upper bounds of approximations by Fourier sums in uniform metric on classes of $2\pi$-periodic functions, representable in the form of convolutions of functions $\varphi$, which belong to unit balls…
We establish asymptotic estimates for exact upper bounds of uniform approximations by Fourier sums on the classes of $2\pi$-periodic functions, which are represented by convolutions of functions $\varphi (\varphi\bot 1)$ from unit ball of…
For functions from the set of generalized Poisson integrals $C^{\alpha,r}_{\beta}L_{p}$, $1\leq p <\infty$, we obtain upper estimates for the deviations of Fourier sums in the uniform metric in terms of the best approximations of the…
The approximation properties of the trigonometric sums U_{n,p}^\psi of a special type are investigated on the classes C^\psi_{\beta, \infty} of (\psi,\beta)-differentiable (in the sense of Stepanets) periodical functions. The solution of…
On the sets of $2\pi$-periodic functions $f$, which are defined with a help of $(\psi, \beta)$-integrals of the functions $\varphi$ from $L_{1}$, we establish Lebesgue-type inequalities, in which the uniform norms of deviations of Fourier…
In metrics of spaces $L_{s}, \ 1\leq s\leq\infty$, we find asymptotic equalities for upper bounds of approximations by Fourier sums on classes of generalized Poisson integrals of periodic functions, which belong to unit ball of space…
We obtain asymptotic equalities for least upper bounds of deviations in the uniform metric of de la Vall\'{e}e Poussin sums on the sets C^{q}_{\beta}H_\omega of Poisson integrals of functions from the class H_\omega generated by convex…
We obtain exact for order estimates of best uniform approximations and uniform approximations by Fourier sums of classes of convolutions the periodic functions belong to unit balls of spaces $L_{p}, \ {1\leq p<\infty}$, with generating…
In metric of spaces $L_{s}, \ 1< s\leq\infty$, we obtain exact order estimates of best approximations and approximations by Fourier sums of classes of convolutions the periodic functions that belong to unit ball of space $L_{1}$, with…
We establish asymptotic estimates for the least upper bounds of approximations in the uniform metric by Fourier sums of order $n-1$ of classes of $2\pi$-periodic Weyl--Nagy differentiable functions, $W^r_{\beta,p}, 1\le p\le \infty,…
We find asymptotic equalities for the exact upper bounds of approximations by Fourier sums of Weyl-Nagy classes $W^r_{\beta,p}, 1\le p\le\infty,$ for rapidly growing exponents of smoothness $r$ $(r/n\rightarrow\infty)$ in the uniform…
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 functions $f$, which are defined by the…
Nikol'skii known theorem for the kernels satisfying a condition $A^*_n$, is proved and for kernels from wider class. Explicit formulas for calculating the value of an approximation of classes $\W^{r, \beta}_{p, n} $ by convolution operators…
We establish estimates for exact upper bounds of deviations of partial Fourier sums $S_{n-1}(f)$ on classes $W^r_{\beta,1}, r>2, \beta\in\mathbb{R},$ of $2\pi$-periodic functions whose $(r,\beta)$-derivatives in the Weyl--Nagy sense belong…
We obtained order estimations for the best uniform approximations by trigonometric polynomials and approximations by Fourier sums of classes of $2\pi$-periodic continuous functions, which $(\psi,\beta)$-derivatives $f_{\beta}^{\psi}$ belong…
In this paper we establish Lebesgue-type inequalities for $2\pi$-periodic functions $f$, which are defined by generalized Poisson integrals of the functions $\varphi$ from $L_{p}$, $1\leq p< \infty$. In these inequalities uniform norms of…
We obtain order-exact estimates for uniform approximations by using Zygmund sums $Z^{s}_{n}$ of classes $C^{\psi}_{\beta,p}$ of $2\pi$-periodic continuous functions $f$ representable by convolutions of functions from unit balls of the space…
We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of $2\pi$-periodic functions $\varphi$, such that $\|\varphi\|_2\le1$, with fixed generated kernels $\Psi_{\bar{\beta}}$,…
In this paper we establish asymptotically best possible interpolation Lebesgue-type inequalities for $2\pi$-periodic functions $f$, which are representable as generalized Poisson integrals of the functions $\varphi$ from the space $L_p$,…
We establish the exact-order estimates of uniform approximations by the Zygmund sums $Z^{s}_{n-1}$ of $2\pi$-periodic continuous functions $f$ from the classes $C^{\psi}_{\beta,p}$.These classes are defined by the convolutions of functions…