On orthorecursive expansions in terms of a chain of systems (Q735856)

Let \(H\) be a separable Hilbert space over \(\mathbb{R}\) or \(\mathbb{C}\). The authors consider an ortholike system \(\{\varphi_k\}\) in \(H\) for which any element \(f \in H\) is represented in the form \(f=\sum_k (f,\varphi_k) \varphi_k\). A complete orthonormal system in \(H\) is a special case of the ortholike systems. The authors introduce the orthorecursive expansion of an element of \(f\), discuss Parseval's identity, and they study expanding subspaces and other related questions.