TY - JOUR
T1 - Convexity analysis and the matrix-valued schur class over finitely connected planar domains
AU - Ball, Joseph A.
AU - Guerra Huamán, Moisés D.
PY - 2013/12/12
Y1 - 2013/12/12
N2 - 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.
AB - 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.
KW - C-convex combination
KW - Choquet theory
KW - Finitely connected planar domain
KW - Interior point of the C-convex hull
KW - Positive operator measures
KW - Schur class
UR - http://www.scopus.com/inward/record.url?scp=84889680684&partnerID=8YFLogxK
U2 - 10.7900/jot.2011sep21.1940
DO - 10.7900/jot.2011sep21.1940
M3 - Artículo (Contribución a Revista)
AN - SCOPUS:84889680684
SN - 0379-4024
VL - 70
SP - 531
EP - 571
JO - Journal of Operator Theory
JF - Journal of Operator Theory
IS - 2
ER -