ORTHORECURSIVE EXPANSION BY THE FABER ? SCHAUDER SYSTEM

Orthorecursive expansions comprise a natural generalization of classical Fourier expansions of Hilbert space elements. For an orthorecursive expansion such properties of normal Fourier series as Bessel identity, Bessel inequality and convergence to the expandable element of Parseval's identity equivalent stand still. In this study orthorecursive expansion by the Faber ? Schauder system is examined, and the theorem of orthorecursive expansion convergence in space is proved.