Properties:: [[good kernel]] Sufficiencies:: *[[Sufficiencies]]* Equivalences:: *[[Equivalences]]* ---- > [!definition] Definition. ([[Fejer Kernel]]) > The $N ^{th}$ **Fejer Kernel** is the average of the first $N$ [[Dirichlet Kernel]]s, $F_{N}(\theta) :=\frac{D_{0} (\theta) + D_{1}(\theta) + \dots + D_{N-1}(\theta)}{\theta} = \frac{1}{N} \frac{\sin ^{2}\left( \frac{N \theta}{2} \right)}{\sin ^{2}\left( \frac{\theta}{2} \right)}, \ \ \theta \in \rr.$ ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```