Definition:Test Function

Definition
Let $\phi : \R^d \to \C$ be a complex-valued function.

Let $\phi$ be a smooth function across its whole domain (including boundaries of support) all its variables.

Let $K \subseteq \R^d$ be a compact subset.

Suppose $\phi$ vanishes outside of $K$:


 * $\forall x \in \R^d \setminus K : \map \phi x = 0$

Then $\phi$ is known as a test function.