Let be a Hilbert space, and suppose is an orthonormal sequence. Then for any ,
Bessel’s inequality immediately lets us define the sum
The inequality means that the series converges.
For a complete orthonormal series, we have Parseval’s theorem, which replaces inequality with equality (and consequently with ).
|Date of creation||2013-03-22 12:46:38|
|Last modified on||2013-03-22 12:46:38|
|Last modified by||ariels (338)|