Fourieranalysis : L^2 projection

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SUMMARY

The discussion focuses on the L^2 projection in Fourier analysis, specifically using the inner product where e_j represents an orthonormal basis. The user sets b_j as for j values ranging from 1 to 3. Despite attempts to refine the solution, the user acknowledges that it remains incorrect and seeks assistance for resolution.

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Schwarzschild90
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Homework Statement


Opgave 14.PNG


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.
 
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Schwarzschild90 said:

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?
 
Hi Ray. Yes and I've developed my solution much more. It's still not quite correct though.
Will someone help me?
Opgave 14 a.PNG
 

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