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Proceedings of the American Mathematical Society

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

 

 

Linear superposition of smooth functions


Author: Robert Kaufman
Journal: Proc. Amer. Math. Soc. 46 (1974), 360-362
MSC: Primary 26A72; Secondary 46E15
MathSciNet review: 0352374
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Abstract: We give a simple proof of the impossibility of representing an arbitrary continuous function as a superposition (1), when $ {F_1}, \cdots ,{F_N}$ are smooth mappings of $ {R^{n + 1}}$ to $ {R^n}$. The main tool is the Riemann-Lebesgue lemma.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0352374-2
Keywords: Smooth functions, Kolmogorov superposition theorem, Baire category
Article copyright: © Copyright 1974 American Mathematical Society