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

  • L. Gogoladze
  • V. Tsagareishvili

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.
Published
25.04.2017
How to Cite
GogoladzeL., and TsagareishviliV. “Convergence of Fourier Series of Functions $\text{Lip} 1$ With respect to General Orthonormal Systems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 4, Apr. 2017, pp. 466-77, http://umj.imath.kiev.ua/index.php/umj/article/view/1710.
Section
Research articles