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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

5 votes
3 answers
2k views

Regarding Kolmogorov's Superposition Theorem

Hi Experts, I have question regarding Kolmogorov's Superposition Theorem: It is known that: Let ${f(x_1,x_2,...,x_m): \Re^m :=[0,1]^m \to \Re}$ be an arbitrary multivariate continuous function. From …
1 vote
0 answers
170 views

Regarding a Feature of Multivariate Real Function

Any real function can be expressed as a function of the sum of two monotonic real functions? More precisely, for real function p(x, y), there exist continuous real functions P(x), h(x,y), g(x) such …
0 votes

Regarding Kolmogorov's Superposition Theorem

Hi AgCl Thank you very much for the reply. It helps to save my time and effort. As this topic is important to me, I want to think about my answer to you carefully. Allow me some days to draft a prope …
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