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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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  • [2] B. L. Fridman, Nowhere denseness of the space of linear superpositions of functions of several variables, Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972), 814–846 (Russian). MR 0318422
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Keywords: Smooth functions, Kolmogorov superposition theorem, Baire category
Article copyright: © Copyright 1974 American Mathematical Society