Editing Parseval's theorem (section)

{{Short description|Theorem in mathematics}}
In mathematics, '''Parseval's theorem''' usually refers to the result that the [[Fourier transform]] is [[Unitary operator|unitary]]; loosely, that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform.<ref>Parseval des Chênes, Marc-Antoine Mémoire sur les séries et sur l'intégration complète d'une équation aux différences partielles linéaire du second ordre, à coefficients constants" presented before the Académie des Sciences (Paris) on 5 April 1799. This article was published in ''Mémoires présentés à l’Institut des Sciences, Lettres et Arts, par divers savants, et lus dans ses assemblées. Sciences, mathématiques et physiques. (Savants étrangers.)'', vol. 1, pages 638–648 (1806).</ref>  It originates from a 1799 theorem about [[series (mathematics)|series]] by [[Marc-Antoine Parseval]], which was later applied to the [[Fourier series]].  It is also known as '''Rayleigh's energy theorem''', or '''Rayleigh's identity''', after [[John William Strutt]], Lord Rayleigh.<ref>Rayleigh, J.W.S. (1889) "On the character of the complete radiation at a given temperature," ''[[Philosophical Magazine]]'', vol. 27, pages 460–469.  Available on-line [https://books.google.com/books?id=izM9AAAAIAAJ&pg=PA268 here].</ref> 

Although the term "Parseval's theorem" is often used to describe the unitarity of ''any'' Fourier transform, especially in [[physics]], the most general form of this property is more properly called the [[Plancherel theorem]].<ref>Plancherel, Michel (1910) "Contribution à l'etude de la representation d'une fonction arbitraire par les integrales définies," ''Rendiconti del Circolo Matematico di Palermo'', vol. 30, pages 298–335.</ref>