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Lookup NU author(s): Professor Jim Agler,
Professor Nicholas Young
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
We generalize to several variables the classical theorem of Nevanlinna that characterizes the Cauchy transforms of positive measures on the real line. We show that for the Loewner class, a large class of analytic functions that have non-negative imaginary part on the upper polyhalfplane, there are representation formulae in terms of densely-defined self-adjoint operators on a Hilbert space. We find four different representation formulae and we show that every function in the Loewner class has one of the four representations, corresponding precisely to four different growth conditions at infinity.
Author(s): Agler J, Tully-Doyle R, Young NJ
Publication type: Article
Publication status: Published
Journal: Journal of Functional Analysis
Print publication date: 15/04/2016
Online publication date: 23/02/2016
Acceptance date: 02/02/2016
Date deposited: 08/03/2016
ISSN (print): 0022-1236
ISSN (electronic): 1096-0783
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