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Krige’s formula. formule de Parseval. Parseval’s equation. formule de Rodrigues. Rodrigues formula. fractal. fractal. fractile quantile. fractile. frequence cumulee. Si on les applique au groupe commutatif fermé à un paramètre des rotations d’un cercle, nos idées contiennent une démonstration de la formule de Parseval.

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Parseval’s theorem

In mathematical analysisParseval’s identitynamed after Marc-Antoine Parsevalis a fundamental result on the summability of the Fourier series of a function. Geometrically, it is the Pythagorean theorem for inner-product spaces.

Informally, the identity asserts that the sum of the squares of the Fourier coefficients of a function is equal to the integral of pareval square of the function. A similar result is the Plancherel theoremwhich asserts that the integral of the square of the Fourier transform of a ;arseval is equal to the integral of the square of the function itself.

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The identity is related to the Pythagorean theorem in the more general setting of a separable Hilbert space as follows. Let e n be an orthonormal basis of H ; i.

Parseval–Gutzmer formula – Wikipedia

This is directly analogous to the Pythagorean theorem, which asserts that the sum of the squares of the components of a vector in an orthonormal basis is equal to the squared length of the vector.

More generally, Parseval’s identity holds in any inner-product spacenot just separable Hilbert spaces. Thus suppose that H is an inner-product space.

Let B be an orthonormal basis of H ; i. The assumption that B is total is necessary for the validity of the identity. This general form of Parseval’s identity can be proved using the Riesz—Fischer theorem. From Wikipedia, the free encyclopedia.

See also [ edit ] Parseval’s theorem References [ edit ] Hazewinkel, Michieled. DeanNumerical Analysis 2nd ed.

Titchmarsh, EThe Theory of Functions 2nd ed. Zygmund, AntoniTrigonometric series 2nd ed. Riesz extension Riesz representation Open mapping Parseval’s identity Schauder fixed-point. Retrieved from ” https: Fourier series Theorems in functional analysis. Views Read Edit View history. This page was last edited on 16 Julyat By using this site, you agree to the Terms of Use and Privacy Policy.