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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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