In mathematics, a square-integrable function, also called a quadratically integrable function or function or square-summable function, [1] is a real - or complex -valued measurable function …

A square integrable function, also called a quadratically integrable function or Class L2 function, is defined as one where the integral of the square of the absolute value is finite (i.e. it can be …

1 day ago · The theory of the square-integrable functions is functional analysis. However, sometimes (e.g. in the context of the Aharonov-Bohm effect), the Hilbert space is taken as the …

Dec 22, 2025 · Informally, an L^2-function is a function f:X->R that is square integrable, i.e., |f|^2=int_X|f|^2dmu with respect to the measure mu, exists (and is finite), in which case |f| is its …

Jun 2, 2023 · Square-integrable functions play a fundamental role in areas of physics such as quantum mechanics, signal processing, and optics. These are functions for which the integral …

Square-integrable functions are those for which the integral of the square of their absolute value over the domain is finite, ensuring membership in the L2 space.

Nov 2, 2017 · A function such that its square has a well-defined integration against a given measure. Last revised on November 2, 2017 at 19:40:52. See the history of this page for a list …

Introduction In this lecture I will present an almost self contained version of two of the most useful tools in the study of Partial Di erential Equ. tions (PDE). These are a Sobolev inequality and a …

In hindsight we can see good reasons that square-integrable functions are connected with energy, and other Physics concepts, but the abstraction seems to have been dictated more out of …

An equivalent definition is to say that the square of the function itself (rather than of its absolute value) is Lebesgue integrable. For this to be true, the integrals of the positive and negative …