Parseval Relation

**frater_cp** · May 31st 2009, 01:39 PM

Derive from $\sum_{k} \vert <x,e_k>\vert ^2 = \|x\|^2$
the following formula which is called the parseval relation:

$<x,y> = \sum_k <x,e_k> \overline{<y,e_k>}.$

**Rebesques** · June 3rd 2009, 08:04 AM

Use the formula $\langle x,y\rangle=\frac{1}{4}\left(||x+y||^2-||x-y||^2\right)-\frac{{\rm i}}{4}\left(||x+{\rm i}y||^2-||x-{\rm i}y||^2\right)$ .

**frater_cp** · June 3rd 2009, 08:08 AM

thank you for the hint! I'll see if I can use it to find the solution to get from A to B

If I get stuck I'll let you know.

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