Orthorecursive expansions generated by the Szegö kernel

This article considers systems of subspaces of the Hardy space generated by the Szegö kernel. The main result of the work is to establish the convergence of orthorecursive expansions with respect to the considered systems of subspaces. Note that the conditions for the convergence of orthorecursive expansions prove to be somewhat more restrictive compared to the previously obtained conditions for the convergence of order-preserving weak greedy algorithms and frame expansions.