Thank you for the response.
Ok, I have proven that this operator is compact. Therefore, it's spectrum consist of set of eigenvalues and 0.
Maybe I messed up the names a bit. I would like to find the kernel of the operator described above. I thought that as the 0 belongs to the spectrum...
Thank you very much.
I managed to find the eigenvalues (4/3, 2/3 +- √5) and eigenvectors for those values.
However, what is still a kind of 'don't-know-what-to-do' problem is how to find eigenvectors for 0, which is also in the spectrum of this operator.
A hint on what to do now would...
Homework Statement
Find spectrum and eigenvalues of operator from L^2(-1,1) to L^2(-1,1)
T(f)(t) = ∫(t+s)^2f(s)ds
The integral is taken over [-1,1]
2. The attempt at a solution
I have already proven that this operator is self-adjoint and compact. However, I have now idea how to find...