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Separation of variables

  1. Oct 6, 2006 #1
    Let be the integral equation:

    [tex] g(s)g(p)g(u)= \int_{0}^{\infty}dx\int_{0}^{\infty}dy\int_{0}^{\infty}dzK(sx)K(py)K(uz)f(x,y,z)

    [/tex]

    then my question is if we could "seek" for a solution in the form:

    [tex] f(x,y,z)=A(x)A(y)A(z) [/tex] where the function A satsify (for x y and z) the integral equation:

    [tex] g(s)=\int_{0}^{\infty}dxK(xs)A(x) [/tex] 8and the same for the other)

    ¿is this approach good?
     
  2. jcsd
  3. Oct 6, 2006 #2

    HallsofIvy

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    Yes, you can- though the general solution may be a linear combination of such solutions.
     
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