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Mat. Sb. (N.S.), 1985, Volume 126(168), Number 3, Pages 420–425 (Mi msb1944)  

This article is cited in 3 scientific papers (total in 3 papers)

On homogeneous polynomials of several variables on the complex sphere

B. S. Kashin


Abstract: This article gives a generalization of a theorem of Ryll and Wojtaszczyk on the existence of a sequence of homogeneous polynomials $P_N$, $N=1,2,…$, in $d$ variables with degree $P_N=N$ for which
$$ \|P_N\|_{L^2(S^d)}\geqslant c_d\|P_N\|_{C(S^d)}>0, $$
where $S^d$ is the sphere in $d$-dimensional complex space.
Bibliography: 11 titles.

Full text: PDF file (262 kB)
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English version:
Mathematics of the USSR-Sbornik, 1986, 54:2, 409–414

Bibliographic databases:

UDC: 517.55
MSC: Primary 32A40; Secondary 32A10
Received: 04.07.1984

Citation: B. S. Kashin, “On homogeneous polynomials of several variables on the complex sphere”, Mat. Sb. (N.S.), 126(168):3 (1985), 420–425; Math. USSR-Sb., 54:2 (1986), 409–414

Citation in format AMSBIB
\Bibitem{Kas85}
\by B.~S.~Kashin
\paper On homogeneous polynomials of several variables on the complex sphere
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 126(168)
\issue 3
\pages 420--425
\mathnet{http://mi.mathnet.ru/msb1944}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=783954}
\zmath{https://zbmath.org/?q=an:0592.32003}
\transl
\jour Math. USSR-Sb.
\yr 1986
\vol 54
\issue 2
\pages 409--414
\crossref{https://doi.org/10.1070/SM1986v054n02ABEH002977}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kashin B., “On One Isometric Operator in l-2 (0.1)”, 38, no. 12, 1985, 1613–1615  mathscinet  zmath  isi
    2. Wojtaszczyk P., “On Values of Homogeneous Polynomials in Discrete Sets of Points”, Studia Math., 84:1 (1986), 97–104  crossref  mathscinet  zmath  isi
    3. Bourgain J., “on Uniformly Bounded Bases in Spaces of Holomorphic Functions”, Am. J. Math., 138:2 (2016), 571–584  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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