|
|
(view preamble)
Cross-references: Riemann integral, place, Lebesgue integral, function, Fourier coefficients, trigonometric functions, interval, integrable functions, square, orthonormal set, difference, inequality, Bessel's inequality, equality, Hilbert space, orthonormal basis
There are 9 references to this entry.
This is version 7 of Parseval equality, born on 2003-09-10, modified 2007-08-30.
Object id is 4717, canonical name is PersevalEquality.
Accessed 10583 times total.
Classification:
| AMS MSC: | 42B05 (Fourier analysis :: Fourier analysis in several variables :: Fourier series and coefficients) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
![$ L^2([-\pi,\pi])$](http://images.planetmath.org:8080/cache/objects/4717/l2h/img6.png "$ L^2([-\pi,\pi])$"){kind=small}
![$ [-\pi,\pi]$](http://images.planetmath.org:8080/cache/objects/4717/l2h/img7.png "$ [-\pi,\pi]$"){kind=small}
![$ [-\pi,\pi]$](http://images.planetmath.org:8080/cache/objects/4717/l2h/img9.png "$ [-\pi,\pi]$"){kind=small}
![$\displaystyle \frac{1}{\pi}\int_{-\pi}^{\pi}f^2(x)dx = \frac{(a_0^f)^2}{2} + \sum_{k=1}^{\infty}[(a_k^f)^2+(b_k^f)^2],$](http://images.planetmath.org:8080/cache/objects/4717/l2h/img11.png "$\displaystyle \frac{1}{\pi}\int_{-\pi}^{\pi}f^2(x)dx = \frac{(a_0^f)^2}{2} + \sum_{k=1}^{\infty}[(a_k^f)^2+(b_k^f)^2],$")
