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Best approximations of integrals by integrals of finite rank
TLDR
We investigate the quantities e σ ( f ) of the best approximation for integrals of functions from the spaces L p ( A , d μ ) by integral of finite rank σ . Expand
On the orders of the best approximations of integrals of functions by integrals of rank σ
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 σExpand
Approximation of functions of several variables by linear methods in the space $S^p$
In the spaces $S^p$ of functions of several variables, $2\pi$-periodic in each variable, we study the approximative properties of operators $A^\vartriangle_{\varrho,r}$ andExpand
On relationship between classes of $(\Psi, \overline\upbeta)$-differentiable functions and Gevrey classes
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 establishExpand
Approximations of certain classes of functions of several variables by greedy approximants in the integral metrics
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 theExpand
Classification of infinitely differentiable periodic functions
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
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 ofExpand
Order estimates of the best $n$-term orthogonal trigonometric approximations of the classes ${\cal F}_{q}^{\psi}$ of periodic functions in the integral metrics
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 coefficientsExpand
On some inequalities of Chebyshev type
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
We obtain necessary and sufficient conditions for validity of some Chebyshev-Type inequalities.
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