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 spectrum. What is have tried is to apply definition (unable to solve integral equation) and the representation in Hilbert space in a form of series.
I am an absolute beginner in functional analysis.
Thank you in advance for any help