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The principal axis theorem for holomorphic functions
Author(s):
Joachim
Gräter;
Markus
Klein
Journal:
Proc. Amer. Math. Soc.
128
(2000),
325-335.
MSC (1991):
Primary 12D15, 12J10, 15A54, 34E10, 81Q15
Posted:
September 27, 1999
MathSciNet review:
1690988
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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.
References:
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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:
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
Posted:
September 27, 1999
Communicated by:
Steven R. Bell
Copyright of article:
Copyright
1999,
American Mathematical Society
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