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