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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2003, Volume 243, Pages 46–52 (Mi tm419)  
Positive Values of Harmonic Polynomials

N. N. Andreeva, V. A. Yudinb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Moscow Power Engineering Institute
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Abstract: 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.
Received in May 2003
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: N. N. Andreev, V. A. Yudin, “Positive Values of Harmonic Polynomials”, Function spaces, approximations, and differential equations, Collected papers. Dedicated to the 70th birthday of Oleg Vladimirovich Besov, corresponding member of RAS, Trudy Mat. Inst. Steklova, 243, Nauka, MAIK «Nauka/Inteperiodika», M., 2003, 46–52; Proc. Steklov Inst. Math., 243 (2003), 39–45
Citation in format AMSBIB
\Bibitem{AndYud03}
\by N.~N.~Andreev, V.~A.~Yudin
\paper Positive Values of Harmonic Polynomials
\inbook Function spaces, approximations, and differential equations
\bookinfo Collected papers. Dedicated to the 70th birthday of Oleg Vladimirovich Besov, corresponding member of RAS
\serial Trudy Mat. Inst. Steklova
\yr 2003
\vol 243
\pages 46--52
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm419}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2049461}
\zmath{https://zbmath.org/?q=an:1124.41026}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2003
\vol 243
\pages 39--45
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