Fejér kernel

Summary

The Fejér kernel $F_N$ is the average of the first $N$ Dirichlet kernels, the trigonometric polynomials that produce the partial sums of a Fourier series. Convolving a periodic function with $F_N$ gives the $N$-th Cesàro mean of its Fourier partial sums. Unlike the Dirichlet kernel, the Fejér kernel is nonnegative, has total mass $1$ and concentrates near $0$. These three properties are the heart of Fejér's theorem.