Signed Measures

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.