Approximation and existence of Schauder bases in Müntz spaces of L1 functions

An approximation of functions in Müntz spaces MΛ,L1MΛ,L1 of L1L1 functions is studied with the help of Fourier series. Müntz spaces are considered with the Müntz condition and the gap condition imposed. It is proved that up to an isomorphism such spaces are contained in Weil–Nagy's class. Moreover, existence of Schauder bases in Müntz spaces MΛ,L1MΛ,L1 is investigated.