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This can not be so easy

  1. Apr 4, 2003 #1
    suppose we want to solve the integral equation

    g(x)=Int(-1,1)exp(-xy)f(y)dy (2) then this is equal to

    g(x)=Int(-infinite,infinite)exp(-xy)f(y)W(y)dy where the W(y) function is defined like that:

    W(y) is 1 iif -1<y<1 and 0 elsewhere.

    then we would have that the equation (2) is a fourier transform and inverting we can get f(x)W(x).

    Is all that?..i can not believe that solving an integral equation could be so easy...
  2. jcsd
  3. Apr 4, 2003 #2


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    Science Advisor

    I'm afraid I don't quite understand your question.

    You refer to g(x)=Int(-1,1)exp(-xy)f(y)dy as an "integral equation" so I presume you mean that g is given and you want to find f.

    How does converting to the integral from -inf to inf make this a Fourier transform? Doesn't the Fourier transform have an exp(-ixy) in it?
  4. Apr 5, 2003 #3
    think he forgot the i in the exp
    but i don't know if you can add the W(y)
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