On the vanishing rate of smooth CR functions

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...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society. Series B 2014-01, Vol.1 (3), p.23-32
Main Authors: Della Sala, Giuseppe, Lamel, Bernhard
Format: Article
Language:English
Subjects:
CR function
exponential decay
Watson Lemma
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Summary: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.]]>
ISSN:2330-1511
2330-1511
DOI:10.1090/S2330-1511-2014-00007-9