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Title: Operator and function theory of the symmetrized polydisc
Author: Ogle, David John
ISNI:       0000 0001 3455 443X
Awarding Body: Newcastle University
Current Institution: University of Newcastle upon Tyne
Date of Award: 1999
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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).
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Operator theory; Interpolation problems