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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
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
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
Linking options:
https://www.mathnet.ru/eng/im2251https://doi.org/10.1070/IM1973v007n02ABEH001941 https://www.mathnet.ru/eng/im/v37/i2/p344
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Abstract page: | 583 | Russian version PDF: | 188 | English version PDF: | 16 | References: | 55 | First page: | 1 |
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