Favard operator

In functional analysis, a branch of mathematics, the Favard operators are defined by:

${\displaystyle [{\mathcal {F}}_{n}(f)](x)={\frac {1}{\sqrt {n\pi }}}\sum _{k=-\infty }^{\infty }{\exp {\left({-n{\left({{\frac {k}{n}}-x}\right)}^{2}}\right)}f\left({\frac {k}{n}}\right)}}$

where ${\displaystyle x\in \mathbb {R} }$, ${\displaystyle n\in \mathbb {N} }$. They are named after Jean Favard.