Quasianalyticity and pluripolarity

We show that the graph \[ Γf={(z,f(z))∈C2:z∈S}\Gamma _f=\{(z,f(z))\in {\mathbb {C}}^2:\,z\in S\} \] in C2{\mathbb {C}}^2 of a function ff on the unit circle SS which is either continuous and quasianalytic in the sense of Bernstein or C∞C^\infty and quasianalytic in the sense of Denjoy is pluripolar....

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Bibliographic Details
Published in:Journal of the American Mathematical Society 2005-04, Vol.18 (2), p.239-252
Main Authors: Coman, Dan, Levenberg, Norman, Poletsky, Evgeny A.
Format: Article
Language:English
Subjects:
Analytic functions
Continuous functions
Greens function
Integers
Mathematical functions
Mathematical theorems
Multipoles
Polynomials
Research article
Subharmonics
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Summary:We show that the graph \[ Γf={(z,f(z))∈C2:z∈S}\Gamma _f=\{(z,f(z))\in {\mathbb {C}}^2:\,z\in S\} \] in C2{\mathbb {C}}^2 of a function ff on the unit circle SS which is either continuous and quasianalytic in the sense of Bernstein or C∞C^\infty and quasianalytic in the sense of Denjoy is pluripolar.
ISSN:0894-0347
1088-6834
DOI:10.1090/S0894-0347-05-00478-9