Parseval's Identity (Paperback)

High Quality Content by WIKIPEDIA articles! In mathematical analysis, Parseval's identity is a fundamental result on the summability of the Fourier series of a function. Geometrically, it is the Pythagorean theorem for inner-product spaces.The identity is related to the Pythagorean theorem in the more general setting of a separable Hilbert space as follows. Suppose that H is a Hilbert space with inner product, . Let (en) be an orthonormal basis of H; i.e., the linear span of the en is dense in H, and the en are mutually orthonormal: More generally, Parseval's identity holds in any inner-product space, not just separable Hilbert spaces. Thus suppose that H is an inner-product space.