Category:Definitions/Schwartz Test Functions
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This category contains definitions related to Schwartz Test Functions.
Related results can be found in Category:Schwartz Test Functions.
Let $\phi : \R \to \C$ be a complex-valued function.
Let $\phi \in \map {C^\infty} \R$ be smooth.
Suppose $\phi$ is bounded in the following way:
- $\ds \forall m, l \in \N : \sup_{x \mathop \in \R} \size {x^l \map {\phi^{\paren m}} x} < \infty$
where $\phi^{\paren m}$ denotes the $m$-th derivative of $\phi$.
Then $\phi$ is known as a Schwartz test function.
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