RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

 Tr. Mat. Inst. Steklova, 2016, Volume 293, Pages 193–200 (Mi tm3713)

On some properties of finite sums of ridge functions defined on convex subsets of $\mathbb R^n$

S. V. Konyagin, A. A. Kuleshov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: Necessary conditions are established for the continuity of finite sums of ridge functions defined on convex subsets $E$ of the space $\mathbb R^n$. It is shown that under some constraints imposed on the summed functions $\varphi _i$, in the case when $E$ is open, the continuity of the sum implies the continuity of all $\varphi _i$. In the case when $E$ is a convex body with nonsmooth boundary, a logarithmic estimate is obtained for the growth of the functions $\varphi _i$ in the neighborhoods of the boundary points of their domains of definition. In addition, an example is constructed that demonstrates the accuracy of the estimate obtained.

 Funding Agency Grant Number Russian Science Foundation 14-50-00005 This work is supported by the Russian Science Foundation under grant 14-50-00005.

DOI: https://doi.org/10.1134/S0371968516020138

Full text: PDF file (199 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 293, 186–193

Bibliographic databases:

Document Type: Article
UDC: 517.518.2
Received: September 18, 2015

Citation: S. V. Konyagin, A. A. Kuleshov, “On some properties of finite sums of ridge functions defined on convex subsets of $\mathbb R^n$”, Function spaces, approximation theory, and related problems of mathematical analysis, Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 293, MAIK Nauka/Interperiodica, Moscow, 2016, 193–200; Proc. Steklov Inst. Math., 293 (2016), 186–193

Citation in format AMSBIB
\Bibitem{KonKul16} \by S.~V.~Konyagin, A.~A.~Kuleshov \paper On some properties of finite sums of ridge functions defined on convex subsets of~$\mathbb R^n$ \inbook Function spaces, approximation theory, and related problems of mathematical analysis \bookinfo Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii \serial Tr. Mat. Inst. Steklova \yr 2016 \vol 293 \pages 193--200 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3713} \crossref{https://doi.org/10.1134/S0371968516020138} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3628479} \elib{http://elibrary.ru/item.asp?id=26344478} \transl \jour Proc. Steklov Inst. Math. \yr 2016 \vol 293 \pages 186--193 \crossref{https://doi.org/10.1134/S0081543816040131} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000380722200013} \elib{http://elibrary.ru/item.asp?id=27119501} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84979966342} 

• http://mi.mathnet.ru/eng/tm3713
• https://doi.org/10.1134/S0371968516020138
• http://mi.mathnet.ru/eng/tm/v293/p193

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. A. Kuleshov, “On some properties of smooth sums of ridge functions”, Proc. Steklov Inst. Math., 294 (2016), 89–94
2. A. A. Kuleshov, “Continuous Sums of Ridge Functions on a Convex Body and the Class VMO”, Math. Notes, 102:6 (2017), 799–805
3. V. E. Ismailov, “A note on the equioscillation theorem for best ridge function approximation”, Expo. Math., 35:3 (2017), 343–349
4. S. V. Konyagin, A. A. Kuleshov, V. E. Maiorov, “Some problems in the theory of ridge functions”, Proc. Steklov Inst. Math., 301 (2018), 144–169
5. Aliev R.A., Asgarova A.A., Ismailov V.E., “A Note on Continuous Sums of Ridge Functions”, J. Approx. Theory, 237 (2019), 210–221
•  Number of views: This page: 199 References: 25 First page: 6