Convergence of Fourier series of functions $\text{Lip} 1$ with respect to general orthonormal systems

• Date: 2017
• Main Authors: Gogoladze, L., Tsagareishvili, V., Гоголадзе, Л., Цагарейшвілі, В.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2017
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1710
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We establish sufficient conditions that should be satisfied by functions of a general orthonormal system (ONS) $\{ \varphi_n(x)\}$ in order that the Fourier series in this system for any function from the class $\mathrm{L}\mathrm{i}\mathrm{p} 1$ be convergent almost everywhere on $[0, 1]$. It is sho...