A superposition theorem for unbounded continuous functions

Author:
Raouf Doss

Journal:
Trans. Amer. Math. Soc. **233** (1977), 197-203

MSC:
Primary 26A72

DOI:
https://doi.org/10.1090/S0002-9947-1977-0582781-1

MathSciNet review:
0582781

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Abstract | References | Similar Articles | Additional Information

Abstract: Let ${R^n}$ be the *n*-dimensional Euclidean space. We prove that there are 4*n* real functions ${\varphi _q}$ continuous on ${R^n}$ with the following property: Every real function *f*, not necessarily bounded, continuous on ${R^n}$, can be written $f(x) = \Sigma _{q = 1}^{2n + 1}g({\varphi _q}(x)) + \Sigma _{q = 2n + 2}^{4n}h({\varphi _q}(x)),x \in {R^n}$, where *g, h* are 2 real continuous functions of one variable, depending on *f*.

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**114**(1957), 953-956; English transl., Amer. Math. Soc. Transl. (2)

**28**(1963), 55-59. MR

**22**#2669;

**27**#3760.

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Keywords:
Superposition of functions,
several variables,
Hilbert Problem 13

Article copyright:
© Copyright 1977
American Mathematical Society