Fejér kernel

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

The Fejér kernel is defined as

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

where Dk(x) is the kth order Dirichlet kernel. It can also be written as

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

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

[edit] See also

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