When is \(f(x_1,x_1,\dots,x_n)= u_1(x_1)+ u_2(x_2)+\cdots+ u_n(x_n)\)?

DOI10.1007/BF02829681zbMath1053.26010arXivmath/0312122MaRDI QIDQ1395915

K. P. S. Bhaskara Rao, A. Kłopotowski, M. G. Nadkarni

Publication date: 22 September 2003

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0312122

zbMATH Keywords

superpositionKolmogorov's theoremgood setlinked componentssequential good measuresequentially good setsimplicial measure

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Representation and superposition of functions (26B40)

Related Items (13)

Diliberto-Straus algorithm for the uniform approximation by a sum of two algebras ⋮ Geometry of good sets in \(n\)-fold Cartesian product ⋮ Approximation by ridge functions and neural networks with a bounded number of neurons ⋮ Some further remarks on good sets ⋮ A note on the equioscillation theorem for best ridge function approximation ⋮ On the representation by sums of algebras of continuous functions ⋮ On the representation by linear superpositions ⋮ Approximation by sums of ridge functions with fixed directions ⋮ On the uniqueness of representation by linear superpositions ⋮ Approximation by neural networks with weights varying on a finite set of directions ⋮ Some remarks on good sets ⋮ On the support of extremal martingale measures with given marginals: the countable case ⋮ A note on the representation of continuous functions by linear superpositions

Cites Work

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• Approximation by a sum of two algebras. The lightning bolt principle
• Uniform separation of points and measures and representation by sums of algebras
• Sur le théorème de superposition de Kolmogorov
• On the existence of automorphisms with simple Lebesgue spectrum
• When is \(f(x,y)=u(x)+v(y)\)?
• Supports of doubly stochastic measures
• On extremal measures and subspace density
• Sums of Subalgebras of C (X )
• Algebra Direct Sum Decomposition of C R (X)
• Algebra Direct Sum Decomposition of C R (X). II
• Uniform approximation by real functions
• Shift invariant measures and simple spectrum
• Sets with doubleton sections, good sets and ergodic theory
• A Remark on Extreme Doubly Stochastic Measures

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