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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Test functions in constrained interpolation


Authors: Michael A. Dritschel and James Pickering
Journal: Trans. Amer. Math. Soc. 364 (2012), 5589-5604
MSC (2010): Primary 47A57; Secondary 32C15, 46E20, 46E22, 47B32
Published electronically: June 8, 2012
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Abstract: We give a set of test functions for $ H_{1}^{\infty }$, the algebra of bounded holomorphic functions on the disk with first derivative equal to 0, whose interpolation problem was studied by Davidson, Paulsen, Raghupathi and Singh (2009). We show that this set of test functions is minimal by relating these ideas to realization and interpolation problems.


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Additional Information

Michael A. Dritschel
Affiliation: Department of Mathematics, University of Newcastle-upon-Tyne, Newcastle-upon-Tyne, NE1 7RU, United Kingdom
Email: m.a.dritschel@ncl.ac.uk

James Pickering
Affiliation: Department of Mathematics, University of Newcastle-upon-Tyne, Newcastle-upon-Tyne, NE1 7RU, United Kingdom
Email: james.pickering@ncl.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05515-2
PII: S 0002-9947(2012)05515-2
Keywords: Interpolation, realizations, Nevanlinna-Pick, test functions
Received by editor(s): April 21, 2009
Published electronically: June 8, 2012
Additional Notes: This paper is based on work contributing to the second author’s Ph.D. thesis, at the University of Newcastle-upon-Tyne, under the supervision of the first author. The work was funded in part by the Engineering and Physical Sciences Research Council.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.