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Matematicheskie Zametki, 2013, Volume 93, Issue 4, Pages 566–574
DOI: https://doi.org/10.4213/mzm9132 (Mi mzm9132) 		 
Interpolation and Superpositions of Multivariate Continuous Functions

S. S. Marchenkov

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm9132
Abstract: 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, superposition, representation, interpolation.
Received: 09.11.2010
Revised: 25.05.2012
English version:
Mathematical Notes, 2013, Volume 93, Issue 4, Pages 571–577
DOI: https://doi.org/10.1134/S0001434613030255
Bibliographic databases:
Document Type: Article
UDC: 519.716
Language: Russian
Citation: S. S. Marchenkov, “Interpolation and Superpositions of Multivariate Continuous Functions”, Mat. Zametki, 93:4 (2013), 566–574; Math. Notes, 93:4 (2013), 571–577
Citation in format AMSBIB
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