Optimal recovery of convolutions of $n$ functions according to linear information

TL;DR

This paper determines the best linear information and methods for recovering convolutions of multiple periodic functions, providing optimal strategies for such function reconstructions.

Contribution

It introduces the optimal linear information and methods for recovering convolutions of multiple functions on periodic classes, advancing the theory of function approximation.

Findings

Identified optimal linear information for convolution recovery

Developed optimal methods for using this information

Achieved theoretical bounds for recovery accuracy

Abstract

We found the optimal linear information and the optimal method of its use to recovery of the convolution of n functions on some classes of $2\pi$ - periodic functions.