2017
Том 69
№ 5

All Issues

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

Gogoladze L., Tsagareishvili V.


Abstract

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 shown that the obtained conditions are best possible in a certain sense.

Citation Example: Gogoladze L., Tsagareishvili V. Convergence of Fourier series of functions $\text{Lip} 1$ with respect to general orthonormal systems // Ukr. Mat. Zh. - 2017. - 69, № 4. - pp. 466-477.