Let $\mathbb{R}^N$ be a
D5630: Set of euclidean real numbers such that
| (i) |
\begin{equation}
\phi : \mathbb{R}^N \to \mathbb{R}, \quad
\phi(x) = e^{- \pi |x|^2}
\end{equation}
|
| (ii) |
$C^{\infty}_c$ is a D392: Set of test functions
|
A
D18: Map $\eta : (0, \infty) \to C^{\infty}_c$ is the
standard mollifier with respect to $\mathbb{R}^N$ if and only if
\begin{equation}
\forall \, \varepsilon > 0 :
\forall \, x \in \mathbb{R}^N :
\eta_{\varepsilon}(x)
= \frac{1}{\varepsilon^N} \phi \left( \frac{x}{\varepsilon} \right)
\end{equation}
