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Eigenvalues of operator between L^2

  1. May 9, 2007 #1
    1. The problem statement, all variables and given/known data

    >M: L_2 -> L_2
    >(Mf)(t) = int(-pi, pi) sin(y-x)f(x) dx
    >how do i find eigenvalues/vectors of M and what can i use to find
    >information about the spectrum?

    2. Relevant equations

    3. The attempt at a solution

    now i know that sin(y-x) = sinycosx-cosysinx
    i also realize that the range is 2dimensional
    when i went to construct f i made it = cosy + asinx
    so i plugged this in, but when i integrated i got 0. did i integrate wrong? or did i take the wrong approach?
  2. jcsd
  3. May 10, 2007 #2
    Can you give the steps that led you to the particular form of f(x) that you have stated?
  4. May 10, 2007 #3
    because i know that the eigenvector is contained in a subspace spanned by sin(x) and cos(x). i figured that'd be a good f?
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