Please use this identifier to cite or link to this item: http://theses.ncl.ac.uk/jspui/handle/10443/1264
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dc.contributor.authorOgle, David John-
dc.date.accessioned2012-06-12T08:38:35Z-
dc.date.available2012-06-12T08:38:35Z-
dc.date.issued1999-
dc.identifier.urihttp://hdl.handle.net/10443/1264-
dc.descriptionPhd Thesisen_US
dc.description.abstractWe establish necessary conditions, in the form of the positivity of Pick-matrices, for the existence of a solution to the spectral Nevanlinna-Pick problem: Let k and n be natural numbers. Choose n distinct points zj in the open unit disc, D, and n matrices Wj in Mk(C), the space of complex k × k matrices. Does there exist an analytic function : D ! Mk(C) such that (zj ) = Wj for j = 1, ...., n and ( (z)) D for all z 2 D? We approach this problem from an operator theoretic perspective. We restate the problem as an interpolation problem on the symmetrized polydisc 􀀀k, 􀀀k = {(c1(z), . . . , ck(z)) | z 2 D} Ck where cj(z) is the jth elementary symmetric polynomial in the components of z. We establish necessary conditions for a k-tuple of commuting operators to have 􀀀k 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 􀀀k.en_US
dc.description.sponsorshipEngineering and Physical Sciences Research Councilen_US
dc.language.isoenen_US
dc.publisherNewcastle Universityen_US
dc.titleOperator and functional theory of the symmetrized polydiscen_US
dc.typeThesisen_US
Appears in Collections:School of Mathematics and Statistics

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