#
nLab

Parseval's theorem

### Context

#### Harmonic analysis

# Contents

## 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..

## 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