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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 294, Pages 99–104
DOI: https://doi.org/10.1134/S0371968516030067 (Mi tm3735) 		 
This article is cited in 7 scientific papers (total in 7 papers)

On some properties of smooth sums of ridge functions

A. A. Kuleshov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (179 kB) Citations (7)
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DOI: https://doi.org/10.1134/S0371968516030067
Abstract: The following problem is studied: If a finite sum of ridge functions defined on an open subset of $\mathbb R^n$ belongs to some smoothness class, can one represent this sum as a sum of ridge functions (with the same set of directions) each of which belongs to the same smoothness class as the whole sum? It is shown that when the sum contains $m$ terms and there are $m-1$ linearly independent directions among $m$ linearly dependent ones, such a representation exists.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.
Received: April 15, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 294, Pages 89–94
DOI: https://doi.org/10.1134/S0081543816060067
Bibliographic databases:
Document Type: Article
UDC: 517.518.2
Language: Russian
Citation: A. A. Kuleshov, “On some properties of smooth sums of ridge functions”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Trudy Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 99–104; Proc. Steklov Inst. Math., 294 (2016), 89–94
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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