Definition:Regular Distribution

Definition

Let $f \in \map {L^1_{loc}} {\R^d}$ be a locally integrable function.

Let $T_f : \map {\DD} {\R^d} \to \C$ be a distribution associated with $f$.

Then $T_f$ is called the regular distribution.

Sources

• 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 6.1$: A glimpse of distribution theory. Test functions, distributions, and examples