Bibliography

1

Jonas Actor. Computation for the Kolmogorov Superposition Theorem. PhD thesis, 2018.

2

Jonas Actor and Matthew G Knepley. An algorithm for computing lipschitz inner functions in kolmogorov’s superposition theorem. arXiv preprint arXiv:1712.08286, 2017.

3

Buma L Fridman. An improvement in the smoothness of the functions in an kolmogorov’s theorem on superpositions. In Doklady Akademii Nauk, volume 177, pages 1019–1022. Russian Academy of Sciences, 1967.

4

T Hedberg. The kolmogorov superposition theorem, appendix ii to hs shapiro, topics in approximation theory. Lecture notes in Math, 187:267–275, 1971.

5

Jean-Pierre Kahane. Sur le theoreme de superposition de kolmogorov. Journal of Approximation Theory, 13(3):229–234, 1975.

6

Jean-Pierre Kahane. Baire’s category theorem and trigonometric series. Journal D’Analyse Mathématique, 80(1):143–182, 2000.

7

JP Kahane. Sur le treizième prohème de hilbert, le théorème de superposition de kolmogorov et les sommes algèbriques d’arcs croissants, in harmonic analysis iraklion 1978 proceedings, 1980.

8

S. Ya Khavinson. Best approximation by linear superpositions (approximate nomography), volume 159. American Mathematical Soc., 1997.

9

Andrei Nikolaevich Kolmogorov. On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition. In Doklady Akademii Nauk, volume 114, pages 953–956. Russian Academy of Sciences, 1957.

10

Hadrien Montanelli and Haizhao Yang. Error bounds for deep relu networks using the kolmogorov–arnold superposition theorem. Neural Networks, 2020.

11

David A Sprecher. An improvement in the superposition theorem of kolmogorov. Journal of Mathematical Analysis and Applications, 38(1):208–213, 1972.

12

Lloyd N Trefethen. Approximation theory and approximation practice, extended edition. SIAM, 2019.

13

Anatoliy Georgievich Vitushkin and GM Khenkin. Linear superpositions of functions. Russian Mathematical Surveys, 22(1):77, 1967.