Square-integrable function

a square-integrable function, also called a quadratically integrable function or L 2 {\displaystyle L^{2}} function or square-summable function, is...

properties of the function spaces of wave functions. In this case, the wave functions are square integrable. One can initially take the function space as the...

almost everywhere, then f {\displaystyle f} is integrable if and only if g {\displaystyle g} is integrable and the integrals of f {\displaystyle f} and...

is equivalent to the Riemann integral. A function is Darboux-integrable if and only if it is Riemann-integrable. Darboux integrals have the advantage of...

transform of an integrable function is continuous and the restriction of this function to any set is defined. But for a square-integrable function the Fourier...

also dense in the space L2(Sn−1) of square-integrable functions on the sphere. Thus every square-integrable function on the sphere decomposes uniquely into...

of square-integrable functions, spaces of sequences, Sobolev spaces consisting of generalized functions, and Hardy spaces of holomorphic functions. Geometric...

Square-integrable function: the square of its absolute value is integrable. Relative to measure and topology: Locally integrable function: integrable around every...

Fourier series is the expansion of a square integrable function into a sum of square integrable orthogonal basis functions. The standard Fourier series uses...

C(G) of continuous complex-valued functions on G, and thus also in the space L2(G) of square-integrable functions. The second part asserts the complete...