The Nevanlinna-Pick interpolation problem in multiply connected domains (Q5941880)

The authors simplify and improve a result of Abrahamse on the Nevanlinna-Pick interpolation problem in a finitely connected domain. According to this result the problem is solvable if and only if the Pick matrices associated with character-automorphic Hardy spaces are positive semidefinite for all characters in \(\mathbb{R}^{n-1}/\mathbb{Z}^{n-1}\), where \(n\) is the connectivity of the domain. The purpose of the paper under review is to reduce the procedure to a proper subset of \(\mathbb{R}^{n-1}/\mathbb{Z}^{n-1}\) whose dimension may be less than \(n-1\).