Parseval's identity


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Parseval's identity

[′pär·sə·vəlz ī′den·əd·ē]
(mathematics)
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Let us study the first term, by Parseval's identity,
Then, by Parseval's identity and Cauchy-Schwartz inequality, we have
Then, using Parseval's identity and Cauchy-Schwartz inequality, we have
By using Parseval's identity, it is possible to get the following set of equations (Appendix A):
The inequalities (97c) and (97d) and Parseval's identity (86) imply that the Fourier coefficients [w.sub.n] = ([w.sub.1n], [w.sub.2n], [w.sub.3n]), n [member of] [N.sub.0], satisfy the estimate
Since [phi] [member of] [{[H.sup.3/2](T)}.sup.2], we see from Parseval's identity that (2.18) implies