I've asked this question both in physics and DSP but I didn't received any useful answer, so I'm trying here:
I have a problem in which I want to find for a given function $t(x,y)$ a function $h(x,y)$ such that: $$ft=f*h$$ for any function $f(x,y)$ sufficiently regular.
Is it a well defined problem with computable solutions? How can I solve this type of problem?
If you want to know the context of the problem you can see my question on DSP: https://dsp.stackexchange.com/questions/36883