Definition:Square Summable Mapping

Definition
Let $\GF$ be a subfield of $\C$.

Let $I$ be a set.

Let $f: I \to \GF$ be a mapping.

Then $f$ is said to be square summable :


 * $\set{ i \in I: \map f i \ne 0 }$ is countable
 * $\ds \sum_{i \mathop \in I} \cmod{ \map f i }^2 < \infty$