Agler, J, Tully-Doyle, R and Young, NJ (2016) Nevanlinna representations in several variables. Journal of Functional Analysis, 270 (8). pp. 3000-3046. ISSN 0022-1236
Abstract
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 identify four types of such representations, and we obtain function-theoretic conditions that are necessary and sufficient for a given function to possess a representation of each of the four types.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | Pick class; Loewner class; Cauchy transform; selfadjoint operator; resolvent |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number EPSRC EP/J004545/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 08 Feb 2016 11:42 |
Last Modified: | 24 Apr 2016 18:17 |
Published Version: | http://dx.doi.org/10.1016/j.jfa.2016.02.004 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jfa.2016.02.004 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:94751 |