(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose we have a physical quantity [tex] f(r) [/tex] depending on another quantity [tex] q(r). [/tex] [tex] f(r) [/tex] is known at all points.

If the following relationship holds:

2. Relevant equations

[tex] f(r)=\int_{\Omega}q(r-r')dr' [/tex]

where [tex] \Omega [/tex] is a bounded volume,

is there any possibility to invert somehow such relationship

in order to have informations on [tex]q(r)[/tex]?

Something like (but not necessarily):

[tex]q(r)=Lf(r)[/tex]

where [tex] L [/tex] is a linear operator.

3. The attempt at a solution

It is a problem similar to that of the Poisson equation, but I should procede

in the opposite way, starting from the integral relationship to get the differential form.

I have already tried to do that but with no success.

This is a textbook like example but I have to say I have no idea whether a solution exists.

(I have not taken it from a book)

Thank you very much to all

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# Homework Help: How to invert an integral equation

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