Recent content by veraguth

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    Spectrum of operator from L^2 to L^2

    that's exactly what I know. Just don't know how to do it.
  2. V

    Spectrum of operator from L^2 to L^2

    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...
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    Spectrum of operator from L^2 to L^2

    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...
  4. V

    Spectrum of operator from L^2 to L^2

    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...
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