Brown, DC, Lykova, ZA and Young, NJ (2017) A rich structure related to the construction of analytic matrix functions. Journal of Functional Analysis, 272 (4). pp. 1704-1754. ISSN 0022-1236
Abstract
We study certain interpolation problems for analytic 2 × 2 matrix-valued functions on the unit disc. We obtain a new solvability criterion for one such problem, a special case of the µ-synthesis problem from robust control theory. For certain domains X in C² and C³ we describe a rich structure of interconnections between four objects: the set of analytic functions from the disc into X , the 2 × 2 matricial Schur class, the Schur class of the bidisc, and the set of pairs of positive kernels on the bidisc subject to a boundedness condition. This rich structure combines with the classical realisation formula and Hilbert space models in the sense of Agler to give an effective method for the construction of the required interpolating functions.
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: | Reproducing kernels; Spectral Nevanlinna–Pick; Symmetrised bidisc; Tetrablock |
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) |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Dec 2016 10:55 |
Last Modified: | 10 May 2019 11:33 |
Published Version: | https://doi.org/10.1016/j.jfa.2016.11.013 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jfa.2016.11.013 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:109050 |