Аннотация:Along with the convergence in L2-norm, convergence almost everywhere
of expansions in functional systems is a property of interest for both theoretical
studies and applications. In this paper we present results on convergence almost
everywhere for orthorecursive expansions which are a natural generalization of classical
expansions in orthogonal systems. As a corollary of a more general result,
we obtain a condition on coefficients of an expansion that guarantees convergence
almost everywhere. We also show that this condition cannot be relaxed.