Geodesic
Positive Values of Harmonic Polynomials
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 46-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that, among all second-order spherical harmonics $Y_2$, the quantity $\mathrm {meas}\{x\in S^2\colon Y_2(x)\ge 0\}$ attains its minimal value at a zonal polynomial. For harmonics of higher even orders, the situation is different. Several examples are considered. 
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N. N. Andreev; V. A. Yudin. Positive Values of Harmonic Polynomials. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 46-52. http://geodesic.mathdoc.fr/item/TM_2003_243_a4/

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