## Just solving for a function [closed]

Given f(x), g(x) can be computed according to the following formula: $g(x) = \int_{-\infty}^{\infty} f(a)f(x-a)da$

I need to find the inverse (a way to compute f(x) given g(x)), and am having no luck. Any ideas would be greatly appreciated.

Thanks!

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You're asking for a way to find out f if you know its convolution with itself (f*f). I'd be very surprised to discover that this was possible - but I don't know enough about convolution to be able to make a definitive statement - so could you please add some explanation as to why you believe that this is possible and what you've done already to try to solve this (and where the problem came from). If the problem isn't simple, then I suspect that the type of function involved will be important so you should add that in as well. – Andrew Stacey Dec 19 2011 at 8:06
Fourier transform? – Gjergji Zaimi Dec 19 2011 at 8:10
More specifically, inverse Fourier transform of a square root of the Fourier transform of g. Whether any choice of square root produces a well-behaved answer will depend. – Robert Israel Dec 19 2011 at 8:17