Abstract
In this chapter the energy problem is generalized to the signed measure case. Suppose that our set ∑ (called a condenser) consists of a finite number of subsets ∑ i on each of which there is a sign and a total charge prescribed for the signed measure. First we show that under these restrictions the energy problem with an external field has a unique solution that is characterized by a self duality property. The weighted equilibrium potential satisfies analogous inequalities and characterization as in the positive measure case.
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© 1997 Springer-Verlag Berlin Heidelberg
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Saff, E.B., Totik, V. (1997). Signed Measures. In: Logarithmic Potentials with External Fields. Grundlehren der mathematischen Wissenschaften, vol 316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03329-6_9
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DOI: https://doi.org/10.1007/978-3-662-03329-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08173-6
Online ISBN: 978-3-662-03329-6
eBook Packages: Springer Book Archive