Fejér kernel

In mathematics, the Fejér kernel is used to express the effect of Cesàro summation on Fourier series. It is a positive kernel, giving rise to an approximate identity.

The Fejér kernel is defined as

<math>F_n(x) = \frac{1}{n} \sum_{k=0}^{n-1}D_k(x),<math>

where <math>D_k(x)<math> is the nth order Dirichlet kernel. It can also be written as

<math>F_n(x) = \frac{1}{n} \frac{(\sin \frac{n x}{2})^2}{(\sin \frac{x}{2})^2}<math>.

It is named for the Hungarian mathematician Lipót Fejér (1880–1959).

See also

• Gibbs phenomenon