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- W39712933 abstract "If E is a compact set in ℂ with cap E >0, then the equilibrium measure μ e minimizes the energy expression $$I[sigma ] = int {{U^sigma }(z)dsigma (z)} $$with respect to all positive Borel measures σ supported on E with σ(E) = 1. Since I[μ e]= − log cap E, the energy I[σ] is positive for all positive Borel measures σ on E if 0 < cap E < 1. Consequently, for such E, $$sigma {(E)^2} leqslant frac{{I[sigma ]}}{{|log capE|}}$$Thus, the total mass σ(E) can be estimated by its energy." @default.
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- W39712933 date "2002-01-01" @default.
- W39712933 modified "2023-09-27" @default.
- W39712933 title "Discrepancy Theorems via Energy Integrals" @default.
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- W39712933 doi "https://doi.org/10.1007/978-1-4757-4999-1_5" @default.
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