# Summation of Fourier series on the infinite dimensional torus

## TL;DR

This paper investigates the convergence conditions of Fejer means for functions on the infinite dimensional torus, extending the results to abstract measure spaces, thus broadening the theoretical understanding of Fourier series convergence.

## Contribution

It provides new convergence criteria for Fejer means on the infinite dimensional torus and generalizes these results to abstract measure spaces.

## Key findings

- Established convergence conditions for square and rectangular Fejer means.
- Generalized convergence results to abstract measure spaces.
- Enhanced theoretical framework for Fourier series on infinite-dimensional structures.

## Abstract

The conditions for convergence of square and rectangular Fejer means of functions on the infinite dimensional torus were obtained, also a generalization of the results for the case of abstract measure spaces was formulated.