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Zapiski Nauchnykh Seminarov POMI, 2008, Volume 353, Pages 139–147
(Mi znsl1638)
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This article is cited in 1 scientific paper (total in 1 paper)
Properties of continuous functions on a normed space and its sphere
V. V. Makeev Saint-Petersburg State University
Abstract:
Known well is the problem of finding configurations of points of the Euclidean sphere $S^n$ that can be put
to one level of any continuous function on $S^n$ by a rotation of $S^n$. The paper is devoted to various ways of transferring this problem to the case of a normed space. Here is one of the results. Let $f$ and $g$ be
two even continuous functions on an $n$-dimensional normed space $E$, and let $f(0)<f(x)$ for each nonzero $x\in E$. Then $E$ contains $n$ unit vectors $e_1,\dots,e_n$ such that for any $1\le i<j\le n$ we have $f(e_i+e_j)=f(e_i-e_j)$ and $g(e_i+e_j)=g(e_i-e_j)$. Bibl. – 16 titles.
Received: 25.01.2007
Citation:
V. V. Makeev, “Properties of continuous functions on a normed space and its sphere”, Geometry and topology. Part 10, Zap. Nauchn. Sem. POMI, 353, POMI, St. Petersburg, 2008, 139–147; J. Math. Sci. (N. Y.), 161:3 (2009), 431–435
Linking options:
https://www.mathnet.ru/eng/znsl1638 https://www.mathnet.ru/eng/znsl/v353/p139
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Abstract page: | 223 | Full-text PDF : | 78 | References: | 25 |
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