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Sibirsk. Mat. Zh., 2018, Volume 59, Number 1, Pages 15–28 (Mi smj2950)  

Recovering linear operators and Lagrange function minimality condition

A. V. Arutyunova, K. Yu. Osipenkobc

a Peoples' Friendship University of Russia, Moscow, Russia
b Lomonosov Moscow State University, Moscow, Russia
c Institute for Information Transmission Problems, Moscow, Russia

Abstract: This article concerns the recovery of the operators by noisy information in the case that their norms are defined by integrals over infinite intervals. We study the conditions under which the dual extremal problem (often nonconvex) can be solved using the Lagrange function minimality condition.

Keywords: optimal recovery, linear operator, extremal problem, Lagrange function.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 02.a03.21.0008
1.962.2017
Russian Foundation for Basic Research 17-51-52022
17-01-00649
Russian Science Foundation 17-11-01168
The authors were supported by the Ministry for Education and Science of Russia (Project 1.962.2017/4.6), the Peoples' Friendship University of Russia (Program 5-100), and the Russian Foundation for Basic Research (Projects 17-51-52022; 18-01-00106; 17-51-12064). Lemmas 1 and 2 and Theorems 1 and 2 were obtained by the first author with the support of the Russian Science Foundation (Project 17-11-01168).


DOI: https://doi.org/10.17377/smzh.2018.59.102

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English version:
Siberian Mathematical Journal, 2018, 59:1, 11–21

Bibliographic databases:

Document Type: Article
UDC: 517.984
MSC: 35R30
Received: 12.03.2017

Citation: A. V. Arutyunov, K. Yu. Osipenko, “Recovering linear operators and Lagrange function minimality condition”, Sibirsk. Mat. Zh., 59:1 (2018), 15–28; Siberian Math. J., 59:1 (2018), 11–21

Citation in format AMSBIB
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\paper Recovering linear operators and Lagrange function minimality condition
\jour Sibirsk. Mat. Zh.
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\vol 59
\issue 1
\pages 15--28
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\crossref{https://doi.org/10.17377/smzh.2018.59.102}
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\jour Siberian Math. J.
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\pages 11--21
\crossref{https://doi.org/10.1134/S0037446618010020}
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