$L^2$ Function

Definition 1: L^2 functions

A complex valued function $f$ is in the class $L^2([a,b]])$ if ${\int }_a^b|f(x){|}^{2}dx$ exists and is finite.

$f$ is in the class $L^2$ if ${\int }_{-\infty }^{\infty }|f(x){|}^{2}dx$ exists and is finite.