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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

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    $ft$ is the pointwise product? Then the left side depends only on data in $(x,y)$, while the right depends on all values from some neighborhood of that point. There can be no equality for general $f$, regardless how regular. For harmonic/holomorphic functions you get something like that with the Cauchy integral formula, you could also look into reproducing kernel Hilbert spaces from the theory of variations. – 2017-01-13
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    Yes, it is the pointwise product. If you rewrite this as an answer I can accept it. – 2017-01-13

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