Affiliation:
1. Yerevan State University, Yerevan, Republic of Armenia
Abstract
We show that if the partial sums $S_{n_i}(x)=\sum_{k=0}^{n_i}a_kf_k(x)$ of a Franklin series $\sum_{k=0}^{\infty}a_kf_k(x)$, where $\sup_i{n_i}/(n_{i-1})<\infty$, converge in measure to a bounded function $f$ and $\sup_i|S_{n_i}(x)|<\infty$ for $ x\not\in B$, where $B$ is some countable set, then this series is the Fourier-Franklin series of $f$.
Bibliography: 24 titles.
Funder
Ministry of Education, Science, Culture and Sports of the Republic of Armenia
Publisher
Steklov Mathematical Institute
Subject
Algebra and Number Theory