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Fundam. Prikl. Mat., 2005, Volume 11, Issue 2, Pages 87–100 (Mi fpm812)  

This article is cited in 2 scientific papers (total in 2 papers)

Extremal problems for linear functionals on the Tchebycheff spaces

V. B. Demidovich, G. G. Magaril-Il'yaev, V. M. Tikhomirov

M. V. Lomonosov Moscow State University

Abstract: The study of the Tchebycheff spaces (generalizing the space of algebraic polynomials) and extremal problems related to them began one and a half centuries ago. Lately, many facts of the approximation theory were understood and reinterpreted from the point of view of general principles of the theory of extremum and convex duality. This approach not only allowed to prove the previously known results for algebraic polynomials and generalized polynomials in a unified way, but also enabled obtaining new results. In this paper, we work out this direction with a special attention to the optimal recovery problems.

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English version:
Journal of Mathematical Sciences (New York), 2007, 142:2, 1923–1932

Bibliographic databases:

UDC: 517

Citation: V. B. Demidovich, G. G. Magaril-Il'yaev, V. M. Tikhomirov, “Extremal problems for linear functionals on the Tchebycheff spaces”, Fundam. Prikl. Mat., 11:2 (2005), 87–100; J. Math. Sci., 142:2 (2007), 1923–1932

Citation in format AMSBIB
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\by V.~B.~Demidovich, G.~G.~Magaril-Il'yaev, V.~M.~Tikhomirov
\paper Extremal problems for linear functionals on the Tchebycheff spaces
\jour Fundam. Prikl. Mat.
\yr 2005
\vol 11
\issue 2
\pages 87--100
\mathnet{http://mi.mathnet.ru/fpm812}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2157931}
\zmath{https://zbmath.org/?q=an:1077.41020}
\elib{http://elibrary.ru/item.asp?id=9068340}
\transl
\jour J. Math. Sci.
\yr 2007
\vol 142
\issue 2
\pages 1923--1932
\crossref{https://doi.org/10.1007/s10958-007-0099-0}
\elib{http://elibrary.ru/item.asp?id=13546688}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33947428439}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. G. Islamov, Yu. V. Kogan, “K voprosu o chebyshevskikh sistemakh”, Izv. IMI UdGU, 2012, no. 1(39), 62–63  mathnet
    2. A. S. Kochurov, V. M. Tikhomirov, “On Extrapolation of Polynomials with Real Coefficients to the Complex Plane”, Math. Notes, 106:4 (2019), 572–576  mathnet  crossref  crossref  isi  elib
  • Фундаментальная и прикладная математика
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