Laplace series

Abstract

In 1900 Leopold Fejér proved his famous theorem concerning the Cesàro summability of the Fourier series of a function defined on the unit circle. In 1908 he proved an analogous result concerning the “Fourier series” of a function defined on the unit sphere: the Laplace series, and in 1925 he considerably sharpened his results. The present article is an expository account of the two papers from 1925.