Convergence of Fourier series of functions $\text{Lip} 1$ with respect to general orthonormal systems - Gogoladze, L.; Tsagareishvili, V. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
We establish sufficient conditions that should be satisfied by functions of a general orthonormal system (ONS) $\{ φ_n(x)\}$in order that the Fourier series in this system for any function from the class $Lip 1$ be convergent almost everywhere on$[0, 1]$. It is shown that the obtained conditions are best possible in a certain sense.