Approximation in M\"untz spaces $M_{\Lambda ,p}$ of $L_p$ functions for $1<p<\infty $ and bases

Abstract

M\"untz spaces satisfying the M\"untz and gap conditions are considered. A Fourier approximation of functions in the M\"untz spaces $M_{\Lambda ,p}$ of $L_p$ functions is studied, where $1<p<\infty $. It is proved that up to an isomorphism and a change of variables these spaces are contained in Weil-Nagy's class. Moreover, existence of Schauder bases in the M\"untz spaces $M_{\Lambda ,p}$ is investigated.