Parseval's theorem


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Parseval's theorem

[′pär·sə·vəlz ′thir·əm]
(mathematics)
A theorem that gives the integral of a product of two functions, ƒ(x) and F (x), in terms of their respective Fourier coefficients; if the coefficients are defined by and similarly for F (x), the relationship is
References in periodicals archive ?
39), along with Parseval's theorem which in the case of the Hankel transform claims that [||h||.
a]) and by Parseval's theorem, this implies the convergence of the sampling series (47) in [L.
1) and Parseval's theorem, it follows by easily that
and by Parseval's theorem again we have the orthogonal decomposition:
We expand the two terms in the inner product in a series of eigenfunctions (5) and use Parseval's theorem.
Finally, an application of Parseval's theorem to the inner product in (11), together with (12) and (13) yields (7).
Applying the Parseval's theorem to the unit function f(x) [equivalent to] with respect to the latter basis, we conclude the well-known identity