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## 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 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