nLab Parseval's theorem

Idea

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..

Related theorems

• Fourier inversion theorem

• Paley-Wiener-Schwartz theorem

References

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