A superposition theorem for unbounded continuous functions
Author:
Raouf Doss
Journal:
Trans. Amer. Math. Soc. 233 (1977), 197203
MSC:
Primary 26A72
MathSciNet review:
0582781
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Abstract: Let be the ndimensional Euclidean space. We prove that there are 4n real functions continuous on with the following property: Every real function f, not necessarily bounded, continuous on , can be written , where g, h are 2 real continuous functions of one variable, depending on f.
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 , Sur le théorème de superposition de Kolmogorov, J. Approximation Theory 13 (1975), 229234. MR 0372134 (51:8351)
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 R. Kaufman, Linear superposition of smooth functions, Proc. Amer. Math. Soc. 46 (1974), 360362. MR 50 #4861. MR 0352374 (50:4861)
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 A. N. Kolmogorov, On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition, Dokl. Akad. Nauk SSSR 114 (1957), 953956; English transl., Amer. Math. Soc. Transl. (2) 28 (1963), 5559. MR 22 #2669; 27 #3760.
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 G. G. Lorentz, Approximations of functions, Holt, Rinehart and Winston, New York, 1966. MR 35 # 4642. MR 0213785 (35:4642)
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 P. A. Ostrand, Dimension of metric spaces and Hilbert's problem 13, Bull. Amer. Math. Soc. 71 (1965), 619622. MR 31 #1654. MR 0177391 (31:1654)
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 D. A. Sprecher, On the structure of continuous functions of several variables, Trans. Amer. Math. Soc. 115 (1965), 340355. MR 35 # 1737. MR 0210852 (35:1737)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197705827811
PII:
S 00029947(1977)05827811
Keywords:
Superposition of functions,
several variables,
Hilbert Problem 13
Article copyright:
© Copyright 1977
American Mathematical Society
