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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A superposition theorem for bounded continuous functions
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by Stephen Demko PDF
Proc. Amer. Math. Soc. 66 (1977), 75-78 Request permission

Abstract:

It is shown that there exist $2n + 1$ real valued, continuous functions ${\phi _0}, \ldots ,{\phi _{2n}}$ defined on ${{\mathbf {R}}^n}$ such that every bounded real valued continuous function on ${{\mathbf {R}}^n}$ is expressible in the form $\Sigma _{i = 0}^{2n}g \circ {\phi _i}$ for some $g \in C({\mathbf {R}})$. Extensions to some unbounded functions are also made.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 66 (1977), 75-78
  • MSC: Primary 26A72
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0457651-5
  • MathSciNet review: 0457651