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

 

On different extremal bases for $ \mathbb{C}$-convex domains


Authors: Nikolai Nikolov, Peter Pflug and Pascal J. Thomas
Journal: Proc. Amer. Math. Soc. 141 (2013), 3223-3230
MSC (2010): Primary 32F17
Published electronically: June 4, 2013
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Abstract: We provide a counterexample (a strongly convex domain in $ \mathbb{C}^3$) to a statement about certain extremal bases in the papers of J. D. McNeal in 1992 and 1994 which was used to prove estimates for the Bergman kernel and invariant metrics. We also prove that those estimates in fact remain correct for the same bases (other authors had introduced different bases to fix this).


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Additional Information

Nikolai Nikolov
Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Email: nik@math.bas.bg

Peter Pflug
Affiliation: Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany
Email: peter.pflug@uni-oldenburg.de

Pascal J. Thomas
Affiliation: Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, F-31062 Toulouse, France
Email: pascal.thomas@math.univ-toulouse.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11584-4
PII: S 0002-9939(2013)11584-4
Keywords: Extremal basis, $\mathbb{C}$-convex domain
Received by editor(s): September 28, 2011
Received by editor(s) in revised form: November 29, 2011, and December 4, 2011
Published electronically: June 4, 2013
Communicated by: Franc Forstneric
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.