Geodesic
On homogeneous polynomials of several variables on the complex sphere
Sbornik. Mathematics, Tome 54 (1986) no. 2, pp. 409-414

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This article gives a generalization of a theorem of Ryll and Wojtaszczyk on the existence of a sequence of homogeneous polynomials $P_N$, $N=1,2,\dots$, 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. 
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     author = {B. S. Kashin},
     title = {On homogeneous polynomials of several variables on the complex sphere},
     journal = {Sbornik. Mathematics},
     pages = {409--414},
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     volume = {54},
     number = {2},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_54_2_a6/}
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B. S. Kashin. On homogeneous polynomials of several variables on the complex sphere. Sbornik. Mathematics, Tome 54 (1986) no. 2, pp. 409-414. http://geodesic.mathdoc.fr/item/SM_1986_54_2_a6/