Definition:Test Function

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

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

Let $K$ be the support of $\phi$:


 * $\map {\operatorname{supp} } \phi = K$

Let $\phi$ be a smooth function across $K$ all its variables.

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

Also known as
Test functions are also known as bump functions.