Linear superposition of smooth functions
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- by Robert Kaufman PDF
- Proc. Amer. Math. Soc. 46 (1974), 360-362 Request permission
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.References
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- 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
- Harold S. Shapiro, Topics in approximation theory, Lecture Notes in Mathematics, Vol. 187, Springer-Verlag, Berlin-New York, 1971. With appendices by Jan Boman and Torbjörn Hedberg. MR 0437981
- David A. Sprecher, An improvement in the superposition theorem of Kolmogorov, J. Math. Anal. Appl. 38 (1972), 208–213. MR 302838, DOI 10.1016/0022-247X(72)90129-1
- A. G. Vituškin and G. M. Henkin, Linear superpositions of functions, Uspehi Mat. Nauk 22 (1967), no. 1 (133), 77–124 (Russian). MR 0237729
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 46 (1974), 360-362
- MSC: Primary 26A72; Secondary 46E15
- DOI: https://doi.org/10.1090/S0002-9939-1974-0352374-2
- MathSciNet review: 0352374