On the vanishing rate of smooth CR functions
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- by Giuseppe Della Sala and Bernhard Lamel HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 1 (2014), 23-32
Abstract:
Let $M$ be a lineally convex hypersurface of $\mathbb C^n$ of finite type, $0\in M$. Then there exist non-trivial smooth CR functions on $M$ that are flat at $0$, i.e. whose Taylor expansion about $0$ vanishes identically. Our aim is to characterize the rate at which flat CR functions can decrease without vanishing identically. As it turns out, non-trivial CR functions cannot decay arbitrarily fast, and a possible way of expressing the critical rate is by comparison with a suitable exponential of the modulus of a local peak function.References
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Additional Information
- Giuseppe Della Sala
- Affiliation: Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria
- MR Author ID: 794044
- Email: giuseppe.dellasala@univie.ac.at
- Bernhard Lamel
- Affiliation: Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria
- MR Author ID: 685199
- ORCID: 0000-0002-6322-6360
- Email: bernhard.lamel@univie.ac.at
- Received by editor(s): April 30, 2013
- Received by editor(s) in revised form: September 2, 2013
- Published electronically: January 13, 2014
- Additional Notes: Both authors were supported by the START Prize Y377 of the Austrian Federal Ministry of Science and Research bmwf. The second author was also supported by the Austrian Science Fund FWF, Project P24878
- Communicated by: Frank Forstneric
- © Copyright 2014 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 1 (2014), 23-32
- MSC (2010): Primary 32V10, 32V20, 32T40
- DOI: https://doi.org/10.1090/S2330-1511-2014-00007-9
- MathSciNet review: 3149613