Convergence of Fourier series of functions 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.