Fourieranalysis : L^2 projection

[Schwarzschild90]

Homework Statement

2. and 3. Relevant equations and the attempt at a solution
We find the L^2 projection as such: $$<b_j , e_j >$$, where e_j is orthonormal basis j.

Now set $$b_j = < x^2 , e_j >$$ for $$1 \leq j \leq 3$$.

 

[Ray Vickson]

Homework Statement

View attachment 107327

2. and 3. Relevant equations and the attempt at a solution
We find the L^2 projection as such: $$<b_j , e_j >$$, where e_j is orthonormal basis j.

Now set $$b_j = < x^2 , e_j >$$ for $$1 \leq j \leq 3$$.

Is there a question in here somewhere?

 

[Schwarzschild90]

Hi Ray. Yes and I've developed my solution much more. It's still not quite correct though.
Will someone help me?