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# 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 Fejer kernel is defined as

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

where

Dk(x)

is the nth order Dirichlet kernel. It is named for the Hungarian mathematician Lipót Fejér (1880–1959).