Trigonometric Approximations and Kolmogorov Widths of Anisotropic Besov Classes of Periodic Functions of Several Variables

2015 ◽  
Vol 66 (8) ◽  
pp. 1248-1266 ◽  
Author(s):  
V. V. Myronyuk
Keyword(s):  
Periodic Functions ◽  
Several Variables ◽  
Kolmogorov Widths

Linear and Kolmogorov widths of the classes B^{\Omega}_{p, \theta} of periodic functions of one and several variables

2020 ◽  
Vol 17 (2) ◽  
pp. 171-187
Author(s):  
Mykhailo Hembars'kyi ◽  
Svitlana Hembars'ka
Keyword(s):  
Periodic Functions ◽  
Several Variables ◽  
Univariate Case ◽  
Kolmogorov Widths

Some estimates exact in order for linear widths of the classes $B^{\Omega}_{p, \theta}$ of periodic multivariable functions in the space $L_q$ with certain relations between the parameters $p$, $q,$ and $\theta$ are obtained. In the univariate case, the estimates exact in order for Kolmogorov and linear widths of the classes $B^{\omega}_{\infty, \theta}$ in the space $L_q$, $1 \leq q \leq \infty,$ are established.

scholarly journals Approximation of smooth periodic functions in several variables

1988 ◽  
Vol 4 (4) ◽  
pp. 356-372 ◽  
Author(s):  
Marek Kowalski ◽  
Waldemar Sielski
Keyword(s):  
Periodic Functions ◽  
Several Variables

scholarly journals Approximation characteristics of the isotropic Nikol'skii-Besov functional classes

2021 ◽  
Vol 13 (3) ◽  
pp. 851-861
Author(s):  
S.Ya. Yanchenko ◽  
O.Ya. Radchenko
Keyword(s):  
Exponential Type ◽  
Lebesgue Space ◽  
Entire Functions ◽  
Exact Order ◽  
Periodic Functions ◽  
Approximation Of Functions ◽  
Several Variables ◽  
Functions Of Exponential Type ◽  
Functional Classes ◽  
Mixed Smoothness

In the paper, we investigates the isotropic Nikol'skii-Besov classes $B^r_{p,\theta}(\mathbb{R}^d)$ of non-periodic functions of several variables, which for $d = 1$ are identical to the classes of functions with a dominant mixed smoothness $S^{r}_{p,\theta}B(\mathbb{R})$. We establish the exact-order estimates for the approximation of functions from these classes $B^r_{p,\theta}(\mathbb{R}^d)$ in the metric of the Lebesgue space $L_q(\mathbb{R}^d)$, by entire functions of exponential type with some restrictions for their spectrum in the case $1 \leqslant p \leqslant q \leqslant \infty$, $(p,q)\neq \{(1,1), (\infty, \infty)\}$, $d\geq 1$. In the case $2<p=q<\infty$, $d=1$, the established estimate is also new for the classes $S^{r}_{p,\theta}B(\mathbb{R})$.

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