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

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Resumen

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.

Idioma originalInglés
Páginas (desde-hasta)531-571
Número de páginas41
PublicaciónJournal of Operator Theory
Volumen70
N.º2
DOI
EstadoPublicada - 12 dic 2013
Publicado de forma externa

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