We establish necessary conditions, in the form of the positivity of Pick-matrices, for the existence of a solution to the spectral Nevanlinna-Pick problem. We approach this problem from an operator theoretic perspective. We restate the problem as an interpolation problem on the symmetrized polydisc Γ(κ). We establish necessary conditions for a κ-tuple of commuting operators to have Γ(κ) as a complete spectral set. We then derive necessary conditions for the existence of a solution of the spectral Nevanlinna- Pick problem. The final chapter of this thesis gives an application of our results to complex geometry. We establish an upper bound for the Caratheodory distance on int Γ(κ).
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:310038 |
| Date | January 1999 |
| Creators | Ogle, David John |
| Publisher | University of Newcastle Upon Tyne |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10443/1264 |
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