# The best approximation of functions from anisotropic Nikol'skii-Besov classes defined in $\mathbb{R}^d$

## TL;DR

This paper derives precise estimates for the best approximation of multivariable functions from anisotropic Nikol'skii-Besov classes by entire functions in Lebesgue spaces, advancing understanding of approximation theory in these function spaces.

## Contribution

It provides the exact-order estimates of best approximations for functions in anisotropic Nikol'skii-Besov classes, a novel result in multivariable approximation theory.

## Key findings

- Established exact-order approximation estimates in Lebesgue spaces.
- Extended approximation theory to anisotropic Nikol'skii-Besov classes.
- Enhanced understanding of function approximation in multivariable settings.

## Abstract

We establish the exact-order estimates of the best approximations of the functions from anisotropic Nikol'skii-Besov classes of several variables by entire functions in the Lebesgue spaces.