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Best approximations of integrals by integrals of finite rank

- A. I. Stepanets, A. L. Shidlich
- Computer Science, Mathematics
- J. Approx. Theory
- 1 February 2010

TLDR

On the orders of the best approximations of integrals of functions by integrals of rank σ

- A. I. Stepanets, A. L. Shidlich
- Mathematics
- 1 October 2007

We study the values eσ(f) of the best approximation of integrals of functions from the spaces Lp(A, dμ) by integrals of rank σ. We determine the orders of the least upper bounds of these values as σ… Expand

Approximation of functions of several variables by linear methods in the space $S^p$

- V. Savchuk, A. L. Shidlich
- Mathematics
- 30 October 2012

In the spaces $S^p$ of functions of several variables, $2\pi$-periodic in each variable, we study the approximative properties of operators $A^\vartriangle_{\varrho,r}$ and… Expand

On relationship between classes of $(\Psi, \overline\upbeta)$-differentiable functions and Gevrey classes

- A. I. Stepanets, A. Serdyuk, A. L. Shidlich
- Mathematics
- 14 July 2009

We investigate the relationship between the classes of $(\Psi, \overline\upbeta)$-differentiable functions introduced by Stepanets and the well-known Gevrey classes. In particular, we establish… Expand

Approximations of certain classes of functions of several variables by greedy approximants in the integral metrics

- A. L. Shidlich
- Mathematics
- 12 February 2013

We find the exact order estimates of the approximations of the classes ${\cal F}_{q,r}^{\psi}$ of functions of several variables by greedy approximants in the integral metric. We also obtain the… Expand

Classification of infinitely differentiable periodic functions

- A. I. Stepanets, A. Serdyuk, A. L. Shidlich
- Mathematics
- 1 December 2008

The set $ \mathcal{D}^\infty $ of infinitely differentiable periodic functions is studied in terms of generalized $ \overline \psi $-derivatives defined by a pair $ \overline \psi = (\psi_1, \psi_2)$… Expand

Approximative Properties of Diagonal Operators in Orlicz Spaces

- A. L. Shidlich, S. Chaichenko
- Mathematics
- 7 May 2014

We obtain the exact values of some important approximative quantities (such as the best approximation, the basis width, Kolmogorov's width, and the best n-term approximation) of certain sets of… Expand

Order estimates of the best $n$-term orthogonal trigonometric approximations of the classes ${\cal F}_{q}^{\psi}$ of periodic functions in the integral metrics

- A. L. Shidlich
- Mathematics
- 28 February 2013

We obtain order estimates in the spaces $L_p$ of the best $n$-term trigonometric orthogonal approximations of the classes ${\cal F}_{q}^{\psi}$ of periodic functions, whose Fourier coefficients… Expand

On some inequalities of Chebyshev type

- A. L. Shidlich, S. Chaichenko
- Mathematics
- 6 May 2014

We obtain some new inequalities of Chebyshev Type. Mathematics subject classification (2010): 26D15.

ON NECESSARY AND SUFFICIENT CONDITIONS FOR VALIDITY OF SOME CHEBYSHEV-TYPE INEQUALITIES

- A. L. Shidlich
- Mathematics
- 2011

We obtain necessary and sufficient conditions for validity of some Chebyshev-Type inequalities.

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