This can not be so easy

  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. HallsofIvy

    HallsofIvy 40,385
    Staff Emeritus
    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. think he forgot the i in the exp
    but i don't know if you can add the W(y)
     
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