On complete characterization of coefficients of a.e. converging orthogonal series

Adam Paszkiewicz

We characterize sequences of numbers $(a_n)$ such that ${\sum }_{n\ge 1}{a}_n{\Phi }_n$ converges a.e. for any orthonormal system $({\Phi }_n)$ in any $L_2$-space. In our criterion, we use the se…