Properties of orthorecursive expansions over nonorthogonal systems (Q1851495)

The author determines the orthorecursive expansions in arbitrary systems which are at most countable in a Hilbert space. These expansions for orthogonal systems coincide with the expansions into Fourier series. The author presents examples of systems of characteristic functions of intervals, in which the orthorecursive expansions of the functions of \(L^p\) classes converge in \(L^p\) and the expansions of the functions integrable in the Denjoy-Perron (Kurzweil-Henstock) sense converge almost everywhere.