Miklós Laczkovich: A superposition theorem of Kolmogorov type for bounded continuous functions

Abstract:

We prove that if  $f\colon {\mathbb R}^n \to {\mathbb R}$ is bounded and continuous, then
$$f(x)=\sum_{q=1}^m g\left( \sum_{p=1}^n \lambda_p \phi _q (x_p ) \right),$$
where $\lambda _1 ,...,\lambda _n$ are positive real numbers and $\phi _1 ,...,\phi _m , g$ are continuous functions of one variable.

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Meeting ID: 937 4669 6898
Passcode: 280561