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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The principal axis theorem
for holomorphic functions


Authors: Joachim Gräter and Markus Klein
Journal: Proc. Amer. Math. Soc. 128 (2000), 325-335
MSC (1991): Primary 12D15, 12J10, 15A54, 34E10, 81Q15
Published electronically: September 27, 1999
MathSciNet review: 1690988
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Abstract | References | Similar Articles | Additional Information

Abstract: An algebraic approach to Rellich's theorem is given which states that any analytic family of matrices which is normal on the real axis can be diagonalized by an analytic family of matrices which is unitary on the real axis. We show that this result is a special version of a purely algebraic theorem on the diagonalization of matrices over fields with henselian valuations.


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Additional Information

Joachim Gräter
Affiliation: Universität Potsdam, Institut für Mathematik, Postfach 601553, 14469 Potsdam, Germany
Email: graeter@rz.uni-potsdam.de

Markus Klein
Affiliation: Universität Potsdam, Institut für Mathematik, Postfach 601553, 14469 Potsdam, Germany
Email: mklein@math.uni-potsdam.de

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05451-9
PII: S 0002-9939(99)05451-9
Keywords: Valuations, Hensel's Lemma, principal axis theorem, analytic perturbation theory
Received by editor(s): March 6, 1998
Published electronically: September 27, 1999
Communicated by: Steven R. Bell
Article copyright: © Copyright 1999 American Mathematical Society