The condition of almost everywhere convergence for a functional series with a weak analogue of the orthonormality property

Moscow University Mathematics Bulletin. 2016. Vol. 71. No. 2. P. 61–67.

V. V. Galatenko, Lukashenko T. P., Sadovnichy V. A.

Переводчик: V. Valedinskii

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.

Ключевые слова: frames, сходимость почти всюду, условие Меньшова-Радемахера, системы Рисса, системы Гильберта, системы Бесселя, фреймы, almost everywhere convergence, Menchoff-Rademacher condition, Riesz systems, Hilbert systems, Bessel systems