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On the structure of representations of continuous functions of several variables as finite sums of continuous functions of one variable


Author: David A. Sprecher
Journal: Proc. Amer. Math. Soc. 17 (1966), 98-105
MSC: Primary 26.55
DOI: https://doi.org/10.1090/S0002-9939-1966-0194565-5
MathSciNet review: 0194565
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References [Enhancements On Off] (What's this?)

  • [1] S. Bochner, Lectures on Fourier integrals, Princeton Univ. Press, Princeton, N. J., 1959; Chapter VI. MR 0107124 (21:5851)
  • [2] 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), 953-956. MR 0111809 (22:2669)
  • [3] A. Ostrovski, Über Dirichletschen Reihen und algebraische Differentialgleichungen, Math. Z. 8 (1920), 241-298. MR 1544442
  • [4] G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis, Problems 119-119(a), 2nd ed., Springer-Verlag, Berlin, 1954, pp. 61-62, 220-223.
  • [5] D. A. Sprecher, On the structure of continuous functions of several variables, Trans. Amer. Math. Soc. 115 (1964), 340-355. MR 0210852 (35:1737)

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DOI: https://doi.org/10.1090/S0002-9939-1966-0194565-5
Article copyright: © Copyright 1966 American Mathematical Society

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