Orthorecursive Fourier-Stieltjes expansions

Orthorecursive Fourier-Stieltjes expansions are defined, and two examples of expansions are considered. The first example deals with orthogonal systems of functions (which include the Haar system as a particular case), and properties of Fourier-Stieltjes expansions in these systems are proved. It is pointed out that in the case of the Haar system, the integrated Fourier-Stieltjes expansion of a continuous function coincides, up to a constant, with the Faber-Schauder series expansion. The second example deals with nonorthogonal systems of functions that are structurally related to the earlier considered orthogonal systems. Properties of orthorecursive Fourier-Stieltjes expansions in these systems are established.