Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Approximation of functions of many variables from the generalization Nikol'skii-Besov type classes in the uniform and integral metrics

M. I. Gromyak, O. Ya. Radchenko, S. Ya. Yanchenko

Abstract

We obtain the exact order estimates of the approximation of the functions of many variables from the generalized Nikol'skii-Besov classes $B^Ω_{p,θ}(\mathbb{R}^d)$ by sums of de la Vallee Poussin type in the metrics space $L_{\infty}(\mathbb{R}^d)$ and $L_{1}(\mathbb{R}^d)$. These classes of functions for some given $Ω$ coincide with the well-known classical Nikol'skii-Besov isotropic classes.

Approximation of functions of many variables from the generalization Nikol'skii-Besov type classes in the uniform and integral metrics

Abstract

We obtain the exact order estimates of the approximation of the functions of many variables from the generalized Nikol'skii-Besov classes by sums of de la Vallee Poussin type in the metrics space and . These classes of functions for some given coincide with the well-known classical Nikol'skii-Besov isotropic classes.
Paper Structure (4 sections, 99 equations)

This paper contains 4 sections, 99 equations.

Table of Contents

  1. Вступ
  2. Основні позначення, означення класів та апроксимаційних характеристик
  3. Наближення частинними сумами типу Валле Пуссена у рівномірній та інтегральній метриках
  4. Acknowledgments

Theorems & Definitions (3)

  • proof
  • proof
  • proof