Fejer kernel

The Fejer kernel Fn of order n is defined as


where Dn is the Dirichlet kernelMathworldPlanetmath of order n. The Fejer kernel can be written as

Fn(t)=1n(sinnt2sint2)2. (1)

Proof: Since


we have



nsin2t2Fn(t) =k=0n-1sin((k+12)t)sint2

From this follows equation (1).

Figure 1: Graphs of some Fejer kernels
Title Fejer kernel
Canonical name FejerKernel
Date of creation 2013-03-22 14:11:56
Last modified on 2013-03-22 14:11:56
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 8
Author mathwizard (128)
Entry type Definition
Classification msc 26A30
Related topic DiracSequence