I am writing the definition of the global maxima of the square of the absolute value of an $L^2$ function, which looks like this:
Here the global maxima is at $x=0$. So I want to make the definition of this global maxima, and I define it as such:
Let $\mathscr{R}f(x)$ denote the range of the force function $f(x)$, and let $|f(x)|$ denote its absolute value. Let $[|(fx)|]^2$ be the square of the absolute value. Then $\text{max}\mathscr{R}[|(fx)|]^2$ is the largest amplitude on the plot of square of the absolute value of $f(x)$.
However, I am not 100% sure this is sufficient. For example defining "the plot" of $f$ is poor language. How can I improve this definition?
Any ideas appreciated