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Quasianalyticity and pluripolarity

Author(s): Dan Coman; Norman Levenberg; Evgeny A. Poletsky
Journal: J. Amer. Math. Soc. 18 (2005), 239-252.
MSC (2000): Primary 26E10, 32U20; Secondary 32U35, 32U15, 32U05
Posted: January 18, 2005
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Abstract: We show that the graph

\begin{displaymath}\Gamma_f=\{(z,f(z))\in{\mathbb{C}}^2:\,z\in S\}\end{displaymath}

in ${\mathbb{C}}^2$ of a function $f$ on the unit circle $S$ which is either continuous and quasianalytic in the sense of Bernstein or $C^\infty$ and quasianalytic in the sense of Denjoy is pluripolar.

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Additional Information:

Dan Coman
Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244
Email: dcoman@syr.edu

Norman Levenberg
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: nlevenbe@indiana.edu

Evgeny A. Poletsky
Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244
Email: eapolets@syr.edu

DOI: 10.1090/S0894-0347-05-00478-9
PII: S 0894-0347(05)00478-9
Keywords: Quasianalytic functions, pluripolar sets, pluripotential theory
Received by editor(s): December 2, 2002
Posted: January 18, 2005
Additional Notes: The first and the last authors were supported by NSF grants
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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