L2 space

An \(L^2\) space is a mathematical environment where functions are considered based on the idea of their "size" or "energy." Specifically, it includes functions whose squares can be integrated (summed up) over a domain and produce a finite value. Think of it as a collection of functions that are "square-integrable," meaning their energy isn't infinite. This space allows mathematicians and engineers to analyze signals, waves, or data in a rigorous way, ensuring that calculations involving these functions are well-defined and stable. It is fundamental in areas like quantum mechanics, signal processing, and data analysis.