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Proceedings of the American Mathematical Society Series B
Proceedings of the American Mathematical Society Series B
ISSN 2330-1511

 

On the vanishing rate of smooth CR functions


Authors: Giuseppe Della Sala and Bernhard Lamel
Journal: Proc. Amer. Math. Soc. Ser. B 1 (2014), 23-32
MSC (2010): Primary 32V10, 32V20, 32T40
Published electronically: January 13, 2014
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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Additional Information

Giuseppe Della Sala
Affiliation: Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria
Email: giuseppe.dellasala@univie.ac.at

Bernhard Lamel
Affiliation: Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria
Email: bernhard.lamel@univie.ac.at

DOI: http://dx.doi.org/10.1090/S2330-1511-2014-00007-9
PII: S 2330-1511(2014)00007-9
Keywords: CR function, exponential decay, Watson Lemma
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
Article copyright: © Copyright 2014 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)