Approximation and Schauder bases in M\"untz spaces $M_{\Lambda ,C}$ of continuous functions

TL;DR

This paper investigates the approximation of functions in M"untz spaces of continuous functions using Fourier series and explores the existence of Schauder bases within these spaces.

Contribution

It provides new insights into Fourier approximation and the existence of Schauder bases in M"untz spaces of continuous functions.

Findings

Fourier series can approximate functions in M"untz spaces.

Conditions for the existence of Schauder bases are established.

Results extend understanding of functional structure in M"untz spaces.

Abstract

In this article M\"untz spaces $M_{\Lambda ,C}$ of continuous functions supplied with the absolute maximum norm are considered. An approximation of functions in M\"untz spaces $M_{\Lambda ,C}$ of continuous functions by Fourier series is studied. An existence of Schauder bases in M\"untz spaces $M_{\Lambda ,C}$ is investigated.