Convexity analysis and matrix-valued Schur class over finitely connected planar domains
Functional Analysis
2011-09-20 v1 Operator Algebras
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.
Keywords
Cite
@article{arxiv.1109.3793,
title = {Convexity analysis and matrix-valued Schur class over finitely connected planar domains},
author = {Joseph A. Ball and Moisés Guerra Huamán},
journal= {arXiv preprint arXiv:1109.3793},
year = {2011}
}
Comments
33 pages