Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol’skii–Besov spaces

Romanyuk, A. S.; Romanyuk, V. S.

doi:10.1007/s10958-020-05177-2

Cited by 2 publications

(2 citation statements)

References 12 publications

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“…Therefore, combining (26), (32), (34) and (36), we get the upper estimate for the trigonometric widths d ⊤ m (B r p,θ , B q,1 ) ≪ m…”

Section: Remarkmentioning

confidence: 95%

“…In the number of papers [2,7,8,11,[24][25][26][27]31], the questions concerning approximation of classes of periodic multivariate functions with mixed smoothness (the classes of Nikol'skii-Besov-type B r p,θ , Sobolev classes W r p,α and some their analogs) in the normed spaces with slightly modified norms comparing to the norm of B q,1 , q ∈ {1, ∞}, were investigated. As a result of the investigations, it was revealed that in many situations the obtained estimates of considered approximative characteristics differ in order from the estimates of corresponding characteristics in the spaces L q , q ∈ {1, ∞}.…”

Section: Introductionmentioning

confidence: 99%

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Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions

Romanyuk

Pozharska

et al. 2023

Carpathian Math. Publ.

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Exact order estimates for some characteristics of linear and nonlinear approximation of the isotropic Nikol'skii-Besov classes $\mathbf{B}^r_{p,\theta}$ of periodic multivariate functions in the spaces $B_{q,1}$, $1\leq q \leq \infty$, are obtained. Among them are the best orthogonal trigonometric approximations, best $m$-term trigonometric approximations, Kolmogorov, linear and trigonometric widths. For all considered characteristics, their estimates coincide in order with the corresponding estimates in the spaces $L_{q}$. Moreover, the obtained exact in order estimates (except the case $1<p<2\leq q < \frac{p}{p-1}$) are realized by the approximation of functions from the classes ${\mathbf{B}}^r_{p,\theta}$ by trigonometric polynomials with the spectrum in cubic regions. In any case, they do not depend on the smoothness parameter $\theta$.

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“…Therefore, combining (26), (32), (34) and (36), we get the upper estimate for the trigonometric widths d ⊤ m (B r p,θ , B q,1 ) ≪ m…”

Section: Remarkmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions

Romanyuk

Pozharska

et al. 2023

Carpathian Math. Publ.

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Найкращі Наближення Класів Періодичних Функцій Багатьох Змінних З Обмеженою Домінуючою Мішаною Похідною

Pozharska,

Romanyuk,

Yanchenko

2024

Ukr. Mat. Zhurn.

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УДК 517.51 Встановлено точні за порядком оцінки наближення класів Соболєва W p , α r ( 𝕋 d ) періодичних функцій багатьох змінних з обмеженою домінуючою мішаною похідною. Наближення здійснюється за допомогою тригонометричних поліномів зі спектром у східчастих гіперболічних хрестах, а похибка оцінюється в метриці простору B q ,1 ( 𝕋 d ) , 1 ≤ p , q < ∞ .

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Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol’skii–Besov spaces

Cited by 2 publications

References 12 publications

Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions

Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions

Найкращі Наближення Класів Періодичних Функцій Багатьох Змінних З Обмеженою Домінуючою Мішаною Похідною

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