Quasianalyticity and pluripolarity
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- by Dan Coman, Norman Levenberg and Evgeny A. Poletsky;
- J. Amer. Math. Soc. 18 (2005), 239-252
- DOI: https://doi.org/10.1090/S0894-0347-05-00478-9
- Published electronically: January 18, 2005
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Abstract:
We show that the graph \[ \Gamma _f=\{(z,f(z))\in {\mathbb {C}}^2: z\in S\}\] 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.References
- Eric Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), no. 1-2, 1–40. MR 674165, DOI 10.1007/BF02392348
- Jean-Pierre Demailly, Mesures de Monge-Ampère et mesures pluriharmoniques, Math. Z. 194 (1987), no. 4, 519–564 (French). MR 881709, DOI 10.1007/BF01161920
- Klas Diederich and John Erik Fornæss, A smooth curve in $\textbf {C}^{2}$ which is not a pluripolar set, Duke Math. J. 49 (1982), no. 4, 931–936. MR 683008, DOI 10.1215/S0012-7094-82-04944-4
- Yitzhak Katznelson, An introduction to harmonic analysis, Second corrected edition, Dover Publications, Inc., New York, 1976. MR 422992
- Maciej Klimek, Pluripotential theory, London Mathematical Society Monographs. New Series, vol. 6, The Clarendon Press, Oxford University Press, New York, 1991. Oxford Science Publications. MR 1150978
- Steven G. Krantz and Harold R. Parks, A primer of real analytic functions, Basler Lehrbücher [Basel Textbooks], vol. 4, Birkhäuser Verlag, Basel, 1992. MR 1182792, DOI 10.1007/978-3-0348-7644-5
- Pierre Lelong, Fonction de Green pluricomplexe et lemmes de Schwarz dans les espaces de Banach, J. Math. Pures Appl. (9) 68 (1989), no. 3, 319–347 (French). MR 1025907
- N. Levenberg, G. Martin, and E. A. Poletsky, Analytic disks and pluripolar sets, Indiana Univ. Math. J. 41 (1992), no. 2, 515–532. MR 1183357, DOI 10.1512/iumj.1992.41.41030
- S. Mandelbrojt, Sur les fonctions indéfiniment dérivables, Acta Math. 72 (1940), 15–29 (French). MR 1783, DOI 10.1007/BF02546326
- W. Pleśniak, Quasianalytic functions in the sense of Bernstein, Dissertationes Math. (Rozprawy Mat.) 147 (1977), 66. MR 427674 [S]Sa A. Sadullaev, Plurisubharmonic Functions, in Several Complex Variables II, Encyclopaedia of Mathematical Sciences, Vol. 8, G. M. Khenkin and A. G. Vitushkin (Editors), Springer, 1994, 59-106.
- A. F. Timan, Theory of approximation of functions of a real variable, International Series of Monographs in Pure and Applied Mathematics, vol. 34, The Macmillan Company, New York, 1963. Translated from the Russian by J. Berry; English translation edited and editorial preface by J. Cossar. MR 192238
Bibliographic Information
- Dan Coman
- Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244
- MR Author ID: 325057
- Email: dcoman@syr.edu
- Norman Levenberg
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 113190
- Email: nlevenbe@indiana.edu
- Evgeny A. Poletsky
- Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244
- MR Author ID: 197859
- Email: eapolets@syr.edu
- Received by editor(s): December 2, 2002
- Published electronically: January 18, 2005
- Additional Notes: The first and the last authors were supported by NSF grants
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 18 (2005), 239-252
- MSC (2000): Primary 26E10, 32U20; Secondary 32U35, 32U15, 32U05
- DOI: https://doi.org/10.1090/S0894-0347-05-00478-9
- MathSciNet review: 2137977