Problems on balayage related to rational interpolation: Research problems \(99-1\) (Q1963852)

Let \(D\) be a bounded simply connected domain in the extended complex plane and \(\Omega\) its complement. The authors consider the probability measures on each domain and at infinity, and corresponding to these measures balayages on the boundary of \(D\). They list some open problems concerning the relations between the balayages, the equilibrium measure for logarithmic potentials of the boundary and approximation by interpolation with polynomials and rational functions.