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

 

The two-by-two spectral Nevanlinna-Pick problem


Authors: Jim Agler and N. J. Young
Journal: Trans. Amer. Math. Soc. 356 (2004), 573-585
MSC (2000): Primary 30E05
Published electronically: September 22, 2003
MathSciNet review: 2022711
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Abstract: We give a criterion for the existence of an analytic $2 \times 2$matrix-valued function on the disc satisfying a finite set of interpolation conditions and having spectral radius bounded by $1$. We also give a realization theorem for analytic functions from the disc to the symmetrised bidisc.


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Additional Information

Jim Agler
Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093

N. J. Young
Affiliation: School of Mathematics and Statistics, University of Newcastle upon Tyne, Merz Court, Newcastle upon Tyne NE1 7RU, England

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03083-6
PII: S 0002-9947(03)03083-6
Received by editor(s): October 9, 2001
Received by editor(s) in revised form: February 26, 2002
Published electronically: September 22, 2003
Additional Notes: This research was supported by an NSF grant in Modern Analysis and an EPSRC Visiting Fellowship
Article copyright: © Copyright 2003 American Mathematical Society