The extremal functional for vector heccextremal logarithmic potential problem with external field and Angelesko matrix of interaction

The aim of the paper is to introduce the new functional, which is defined on vector compact sets. The functional has the extremal point on the support of the equilibrium measure for vector extremal logarithmic potential problem with an external field Angelesko matrix of interaction and any positive total masses of components. We will show how to use the functional by extremal problem for two intervals with common endpoint.