# Inverting an integral transform

This question is either very obvious or by nature unsolvable in a general case. I Google'd around for a solution to no avail.

Given an integral transform of kernel K across some interval I as a subset of reals, what is the method for find the inverse kernel K^-1 of some interval H? Obviously an inverse does not exist in all cases (eg K(t,s) = 0 ), but is there some general method for finding one if it does?

I found some interesting information on the dirac delta function, but the only expressions I was able to deduce from it were useless.

Thanks for you help!

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Can you give an example, where $K$ and $K^{-1}$ exists? – draks ... Apr 4 '12 at 21:49
To be honest, I'm not so much concerned with specific cases, rather I'm interested in a general method to deduce an inverse kernel from its compliment. Further expanding upon my naiveity, I don't know how to know when an inverse kernel exists. It seems reasonable to me that the kernel K[t,s] = t^s over the interval (0,1) should define a unique integral transform. How would one go about "solving" for an inverse? – Alec Apr 18 '12 at 23:28