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The Nevanlinna-Pick interpolation problem in multiply connected domains. (English. Russian original) Zbl 0997.47014

J. Math. Sci., New York 105, No. 4, 2109-2126 (2001); translation from Zap. Nauchn. Semin. POMI 254, 5-27 (1998).
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 \(n-1\).

MSC:

47A57 Linear operator methods in interpolation, moment and extension problems
30E05 Moment problems and interpolation problems in the complex plane
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