- Fejér kernel
mathematics, the Fejér kernel is used to express the effect of Cesàro summationon Fourier series. It is a non-negative kernel, giving rise to an approximate identity.
The Fejér kernel is defined as
where is the "k"th order
Dirichlet kernel. It can also be written in a closed form as
where this expression is defined. It is named after the Hungarian mathematician
The important property of the Fejér kernel is . The
convolution"Fn" is positive: for of period it satisfies
and, by the
Hölder's inequality, for every or continuous function ;moreover, for every () or continuous function .
Charles Jean de la Vallée-Poussin
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