Optimal recovery problems on the classes that are determined by restrictions on several higher derivatives of the functions

TL;DR

This paper addresses optimal approximation and interpolation for periodic functions constrained by multiple higher derivative restrictions, providing solutions to these classical problems in approximation theory.

Contribution

It introduces new solutions for optimal recovery problems on classes of periodic functions defined by higher derivative restrictions, advancing approximation theory.

Findings

Derived explicit solutions for optimal recovery problems.

Extended classical approximation results to functions with multiple derivative constraints.

Enhanced understanding of approximation limits for higher derivative-restricted classes.

Abstract

Optimal approximation and optimal interpolation problems on the classes of periodic functions that are determined by restrictions on several higher derivatives of the functions are solved.