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Green function as distributions

  1. Jan 5, 2012 #1
    If we have Green function

    [tex]g(x,s)=exp[-\int^x_s p(z)dz][/tex] we want to think about that as distribution so we multiply it with Heaviside step function

    [tex]g(x,s)=H(x-s)exp[-\int^x_s p(z)dz][/tex]

    Why we can just multiply it with step function and tell that the function is the same. Tnx for the answer.
     
  2. jcsd
  3. Jan 5, 2012 #2
    To be more precise.

    If I say solution to eq is

    [tex]u(x)=\int^{x}_0g(x,s)f(s)ds[/tex]

    where [tex]g=e^{-\int^x_yp(z)dz}[/tex]

    Then if I define

    [tex]g=H(x-s)e^{-\int^x_sp(z)dz}[/tex]

    is then

    [tex]u(x)=\int^{\infty}_0g(x,s)f(s)ds[/tex]

    and what is Green function this [tex]g=e^{-\int^x_yp(z)dz}[/tex] or this [tex]g=H(x-s)e^{-\int^x_sp(z)dz}[/tex]?
     
  4. Jan 7, 2012 #3
    Can you help me?
     
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