The Condition of Almost Everywhere Convergence for a Functional Series with a Weak Analogue of the Orthonormality Property / V. V. Galatenko, T. P. Lukashenko, and V. A. Sadovnichii. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 2. P. 18-24 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 61-67].
The almost everywhere convergence condition similar to the Menchoff–Rademacher condition is obtained for functional series with some weak analogue of the orthogonality property. As a corollary, results related to almost everywhere convergence of series with respect to Riesz systems, Hilbert and Bessel systems, and frames are obtained.
Key words: almost everywhere convergence, Menchoff–Rademacher condition, Riesz systems, Hilbert systems, Bessel systems, frames.