This paper continues the investigation of representations of continuous functions f( X 1 ..... Xn) with n .... > 2 in the form f( x~, , Xn ) = ~ q=O2n Xqt a~ f z\_,S" P=n I Xp ~b( Xp + qe,) ] with a predetermined function ~b that is independent of n. The fimction ~k is defined through its graph that
On a Constructive Proof of Kolmogorov’s Superposition Theorem
✍ Scribed by Jürgen Braun; Michael Griebel
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 625 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0176-4276
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📜 SIMILAR VOLUMES
Gleason's theorem states that any totally additive measure on the closed subspaces, or projections, of a Hilbert space of dimension greater than two is given by a positive operator of trace class. In this paper we give a constructive proof of that theorem.
Based on constructions of Kolmogorov and an earlier refinement 0/ the author, we lise a sequence of integrally independent positive numbers to construct a continuousfunction -./I( x) having thefollowing property: Every real-valued uniformly continuous function f( XI • . . . • x n) of n ~2 variables