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

• Datum: 2017
• Hauptverfasser: Gogoladze, L., Tsagareishvili, V., Гоголадзе, Л., Цагарейшвілі, В.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2017
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/1710
• Назва журналу: 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...