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Use of Dirac delta to define an inverse

  1. Dec 14, 2011 #1
    I was wondering which are the properties of functions defined in such a way that

    ∫dx f(y-x) g(x-z) = δ(y-z)

    where δ is Dirac delta and therefore g is a kind of inverse function of f (I see this integral
    as the continuous limit of the product of a matrix by its inverse, in which case the δ becomes the identity matrix). Does anyone know where this type of "inverse functions" are
    discussed? or how to obtain the function g given f ?
     
  2. jcsd
  3. Dec 18, 2011 #2
    update:

    I found that taking the Fourier transform of both sides one can show that
    g(y)=∫dk (1/f(k)) eikx
    up to some factor of 2π, where f(k) is the Fourier transform of f(x).
     
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