In harmonic analysis, *Parseval’ theorem* states that Fourier transform is a unitary operator.

For Fourier transform over Cartesian spaces see e.g. Hörmander 90, theorem 7.1.6, this prop..

For Fourier transform over Cartesian spaces:

- Lars Hörmander, theorem 7.1.6 of
*The analysis of linear partial differential operators*, vol. I, Springer 1983, 1990

See also

- Wikipedia,
*Parseval’s theorem*

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