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Mathematics of the USSR-Izvestiya, 1973, Volume 7, Issue 2, Pages 345–356
DOI: https://doi.org/10.1070/IM1973v007n02ABEH001941
(Mi im2251)
 

This article is cited in 18 scientific papers (total in 18 papers)

On an extremal problem for polynomials in $n$ variables

Yu. A. Brudnyi, M. I. Ganzburg
References:
Abstract: This article is devoted to an examination of the following extremal problem: find the quantity
$$ C_{k,n}(\lambda,B)=\sup_{|\omega|\ge\lambda}\sup_{P\in\mathscr P_{k,n}(\omega)}\|P\|_{C(B)}, $$
where $B$ is an $n$-dimensional sphere and $\mathscr P_{k,n}(\omega)$ is the totality of polynomials $P$ of degree $k$ in $n$ variables for which $\|P\|_{C(\omega)}\le1$. Here $\omega$ is a measurable set from $B$ and the first sup is taken over all measurable $\omega\subset B$ having measure $|\omega|\ge\lambda$.
The exact order of growth of $C_{k,n}(\lambda, B)$ which respect to $\lambda$ as $\lambda\to0$ is found in this article. Various applications of the results are examined as well.
Received: 31.05.1971
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1973, Volume 37, Issue 2, Pages 344–355
Bibliographic databases:
UDC: 577.514
MSC: Primary 41A10, 41A63; Secondary 41A50
Language: English
Original paper language: Russian
Citation: Yu. A. Brudnyi, M. I. Ganzburg, “On an extremal problem for polynomials in $n$ variables”, Izv. Akad. Nauk SSSR Ser. Mat., 37:2 (1973), 344–355; Math. USSR-Izv., 7:2 (1973), 345–356
Citation in format AMSBIB
\Bibitem{BruGan73}
\by Yu.~A.~Brudnyi, M.~I.~Ganzburg
\paper On an extremal problem for polynomials in~$n$ variables
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 2
\pages 344--355
\mathnet{http://mi.mathnet.ru/im2251}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=352825}
\zmath{https://zbmath.org/?q=an:0283.26012}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 2
\pages 345--356
\crossref{https://doi.org/10.1070/IM1973v007n02ABEH001941}
Linking options:
  • https://www.mathnet.ru/eng/im2251
  • https://doi.org/10.1070/IM1973v007n02ABEH001941
  • https://www.mathnet.ru/eng/im/v37/i2/p344
  • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:583
    Russian version PDF:188
    English version PDF:16
    References:55
    First page:1
     
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