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Mat. Zametki, 2013, Volume 93, Issue 4, Pages 566–574 (Mi mz9132)  

Interpolation and Superpositions of Multivariate Continuous Functions

S. S. Marchenkov

M. V. Lomonosov Moscow State University

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.

DOI: https://doi.org/10.4213/mzm9132

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English version:
Mathematical Notes, 2013, 93:4, 571–577

Bibliographic databases:

UDC: 519.716
Received: 09.11.2010
Revised: 25.05.2012

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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