Convexity analysis and the matrix-valued schur class over finitely connected planar domains

Research output: Contribution to journalArticle (Contribution to Journal)

5 Scopus citations

Abstract

We identify the set of extreme points and apply Choquet theory to a normalized matrix-measure ball subject to finitely many linear side constraints. As an application we obtain integral representation formulas for the Herglotz class of matrix-valued functions on a finitely-connected planar domain and associated continuous Agler decompositions for the matrix-valued Schur class over the domain. The results give some additional insight into the negative answer to the spectral set problem over such domains recently obtained by Agler-Harland-Raphael and Dritschel-McCullough.

Original languageEnglish
Pages (from-to)531-571
Number of pages41
JournalJournal of Operator Theory
Volume70
Issue number2
DOIs
StatePublished - 12 Dec 2013
Externally publishedYes

Keywords

  • C-convex combination
  • Choquet theory
  • Finitely connected planar domain
  • Interior point of the C-convex hull
  • Positive operator measures
  • Schur class

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