Geodesic
Interpolation and Superpositions of Multivariate Continuous Functions
Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 566-574

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A new approach to proving the unrepresentability of multivariate continuous functions by superpositions of continuous functions of fewer variables is suggested. The approach is based on the idea of interpolating functions with the use of sufficiently sparse interpolation nodes but with relatively high accuracy. The approach is illustrated by Vitushkin's well-known results on superpositions of functions that depend on a given number of variables and have derivatives of a given order.
Keywords: multivariate function, continuous function, representation
Mots-clés : superposition, interpolation. 
@article{MZM_2013_93_4_a7,
     author = {S. S. Marchenkov},
     title = {Interpolation and {Superpositions} of {Multivariate} {Continuous} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {566--574},
     publisher = {mathdoc},
     volume = {93},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a7/}
}
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S. S. Marchenkov. Interpolation and Superpositions of Multivariate Continuous Functions. Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 566-574. http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a7/