Definition:Delta Sequence

Definition
Let $\sequence {\map {\delta_n} x}_{n \mathop \in \N}$ be a sequence of continuous real-valued functions.

Let $\phi \in \map {\CC^\infty} \R$ be a smooth function with a compact support.

Suppose:


 * $\ds \lim_{n \mathop \to \infty} \int_{-\infty}^\infty \map {\delta_n} x \map \phi x = \map \phi 0$

Then $\sequence {\map {\delta_n} x}_{n \mathop \in \N}$ is called the delta sequence.