On different extremal bases for $\mathbb {C}$-convex domains
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- by Nikolai Nikolov, Peter Pflug and Pascal J. Thomas PDF
- Proc. Amer. Math. Soc. 141 (2013), 3223-3230 Request permission
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).References
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Additional Information
- Nikolai Nikolov
- Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
- MR Author ID: 332842
- Email: nik@math.bas.bg
- Peter Pflug
- Affiliation: Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany
- MR Author ID: 139035
- 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
- MR Author ID: 238303
- Email: pascal.thomas@math.univ-toulouse.fr
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 3223-3230
- MSC (2010): Primary 32F17
- DOI: https://doi.org/10.1090/S0002-9939-2013-11584-4
- MathSciNet review: 3068975