Cesàro means of Fourier series

Summary

The Cesàro means of a Fourier series are the averages of its first $N$ partial sums. They equal the convolution of the function with the Fejér kernel, a positive summability kernel. For this reason they behave much better than the partial sums: by Fejér's theorem they converge uniformly for every continuous periodic function. They are the Cesàro mean of the sequence of partial sums.