A superposition theorem for unbounded continuous functions
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- by Raouf Doss PDF
- Trans. Amer. Math. Soc. 233 (1977), 197-203 Request permission
Abstract:
Let ${R^n}$ be the n-dimensional Euclidean space. We prove that there are 4n 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.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- 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