- #1
nista
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Homework Statement
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:
Homework 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.
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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