How to represent simple multiplications as additions?

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According to Kolmogorov–Arnold representation theorem any multivariate function can be represented as sum of univariate functions.

This should hold for multiplications too, so

$xy = F(x) + G(y)$

$xyz = F(x) + G(y) + H(z)$

and so on. Are there any simple examples of F, G, and H?


Ah, I thought in

$\sum_{q=0}^{2n} \Phi_{q}\left(\sum_{p=1}^{n} \phi_{q,p}(x_{p})\right)$

$\Phi_{q}$

is a coefficient, while it is a function.

Okay please help to find an example of

$xy = \Phi(\phi_1(x) + \phi_2(y))$

then