Operator-valued Herglotz kernels and functions of positive real part on the ball

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dc.creatorJury, Michael T.
dc.date2008-01-02
dc.date.accessioned2026-07-07T08:52:15Z
dc.date.available2026-07-07T08:52:15Z
dc.descriptionWe describe several classes of holomorphic functions of positive real part on the unit ball; each is characterized by an operator-valued Herglotz formula. Motivated by results of J.E. McCarthy and M. Putinar, we define a family of weighted Cauchy-Fantappiè pairings on the ball and establish duality relations between certain pairs of classes, and in particular we identify the dual of the positive Schur class. We also establish the existence of self-dual classes with respect to this pairing, and identify some extreme points of the positive Schur class.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0801.0438
dc.identifierhttp://arxiv.org/abs/0801.0438
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145216
dc.subjectFunctional Analysis
dc.subjectComplex Variables
dc.subject32A26, 47A56
dc.titleOperator-valued Herglotz kernels and functions of positive real part on the ball
dc.typetext

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