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

MathSciNet review:
2946923

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give a set of test functions for , 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

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.