Summon of Fejér

In Mathematical, in analyzes functional and harmonic, one calls nap of Fejér of order N the function obtained by making the Moyenne of Cesàro N first sums partial of Fourier:

$\backslash \; varphi\_n\; =\; \backslash \; frac\; \{1\}\; \{N\}\; \backslash \; left\; (S\_0\; +\; \backslash \; ldots\; +\; S\_\; \{n-1\}\; \backslash \; right)$

One can also obtain this sum by convolution Noyau of Fejér with the function. According to Theorem of Fejér, if F is continuous, then the continuation of its sums of Fejér converges uniformly towards F . If it is continuous per pieces, the sum converges towards regularized F .

Contrary to the Fourier series, the sums of Fejér do not post the Phénomène of Gibbs.

See too

• Fourier series;
• Phenomenon of Gibbs;
• Core of Fejér;
• Theorem of Fejér;

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