Use of Dirac delta to define an inverse

  • Thread starter lukluk
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  • #1
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Main Question or Discussion Point

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 ?
 

Answers and Replies

  • #2
8
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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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