On the structure of continuous functions of several variables
Author:
David A. Sprecher
Journal:
Trans. Amer. Math. Soc. 115 (1965), 340355
MSC:
Primary 26.55
MathSciNet review:
0210852
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References 
Similar Articles 
Additional Information
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 V. I. Arnol'd, On functions of three variables, Dokl. Akad. Nauk SSSR 114 (1957), 953956. MR 0111809 (22:2669)
 [2]
 , The representation of functions of several variables, Mat. Prosvešč 3 (1958), 4161.
 [3]
 D. Hilbert, Mathematical problems, Bull. Amer. Math. Soc. 8 (1902), 461462. MR 1557926
 [4]
 , Über die Gleichung neunten Grades, Math. Ann. 97 (1927), 243250. MR 1512361
 [5]
 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), 369373. MR 0111809 (22:2669)
 [6]
 G. G. Lorentz, Metric entropy, widths, and superpositions of functions, Amer. Math. Monthly 69 (1962), 469485. MR 0141926 (25:5323)
 [7]
 T. Schneider, Einführung in die transzendenten Zählen, Springer, Berlin, 1957. MR 0086842 (19:252f)
 [8]
 D. A. Sprecher, A representation theorem for continuous functions of several variables, Proc. Amer. Math. Soc. 16 (1965), 200203. MR 0174666 (30:4866)
 [9]
 V. M. Tihomirov, The works of A. N. Kolmogorov on entropy of function classes and superpositions of functions, Uspehi Mat. Nauk 18 (1963), no. 5 (113), 5592. MR 0162910 (29:214)
 [10]
 A. G. Vituškin, On Hilbert's thirteenth problem, Dokl. Akad. Nauk SSSR 95 (1954), 701704.
 [11]
 D. A. Sprecher, On the structure of representations of continuous functions of several variables as finite sums of continuous functions of one variable, (to appear). MR 0194565 (33:2775)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994719650210852X
PII:
S 00029947(1965)0210852X
Article copyright:
© Copyright 1965
American Mathematical Society
