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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Boundary behavior of infinitesimal generators in the unit ball


Authors: Filippo Bracci and David Shoikhet
Journal: Trans. Amer. Math. Soc. 366 (2014), 1119-1140
MSC (2010): Primary 37L05; Secondary 32A40, 20M20
Published electronically: September 19, 2013
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Abstract: We prove a Julia-Wolff-Carathéodory type theorem for infinitesimal generators on the unit ball in $ \mathbb{C}^{n}$. Moreover, we study jets expansions at the boundary and give necessary and sufficient conditions on such jets for an infinitesimal generator to generate a group of automorphisms of the ball.


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Additional Information

Filippo Bracci
Affiliation: Dipartimento Di Matematica, Università di Roma “Tor Vergata”, Via Della Ricerca Scientifica 1, 00133, Roma, Italy
Email: fbracci@mat.uniroma2.it

David Shoikhet
Affiliation: Department of Mathematics, ORT Braude College, 21982 Karmiel, Israel
Email: davs@braude.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05996-X
PII: S 0002-9947(2013)05996-X
Keywords: Infinitesimal generators, semigroups of holomorphic mappings, Julia-Wolff-Carath\'eodory theorem, boundary rigidity
Received by editor(s): March 8, 2012
Received by editor(s) in revised form: September 22, 2012
Published electronically: September 19, 2013
Additional Notes: The first author was partially supported by the ERC grant “HEVO - Holomorphic Evolution Equations” n. 277691
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.