Geodesic
Green energy of discrete signed measure on concentric circles
Izvestiya. Mathematics , Tome 87 (2023) no. 2, pp. 265-283

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We show that the difference between the Green energy of a discrete signed measure relative to a circular annulus concentrated at some points on concentric circles and the energy of the signed measure at symmetric points is non-decreasing during the expansion of the annulus. As a corollary, generalizations of the classical Pólya–Schur inequality for complex numbers are obtained. Some open problems are formulated.
Keywords: Green function, Green energy, capacity of condensers, dissymmetrization, inequality. 
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     author = {V. N. Dubinin},
     title = {Green energy of discrete signed measure on concentric circles},
     journal = {Izvestiya. Mathematics },
     pages = {265--283},
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     volume = {87},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2023_87_2_a2/}
}
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V. N. Dubinin. Green energy of discrete signed measure on concentric circles. Izvestiya. Mathematics , Tome 87 (2023) no. 2, pp. 265-283. http://geodesic.mathdoc.fr/item/IM2_2023_87_2_a2/