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ISSN 1088-6826(e) ISSN 0002-9939(p)

A residual radial limit zero set

Author(s): Michael C. Fulkerson
Journal: Proc. Amer. Math. Soc. 137 (2009), 3725-3731.
MSC (2000): Primary 32A40
Posted: June 15, 2009
MathSciNet review: 2529880
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Abstract | References | Similar articles | Additional information

Abstract: We construct a nonconstant holomorphic function on the unit ball in $\mathbb{C}^n$ having radial limit zero on a certain residual subset of the unit sphere.

References:

1.: Robert D. Berman, A converse to the Lusin-Privalov radial uniqueness theorem, Proc. Amer. Math. Soc. 87 (1983), no. 1, 103-106. MR 677242 (84m:30048)
2.: Monique Hakim and Nessim Sibony, Boundary properties of holomorphic functions in the ball of ${\bf C}\sp n$ , Math. Ann. 276 (1987), no. 4, 549-555. MR 879534 (88c:32008)
3.: N. Lusin and J. Priwaloff, Sur l'unicité et la multiplicité des fonctions analytiques, Ann. Sci. École Norm. Sup. (3) 42 (1925), 143-191. MR 1509265
4.: J. E. McMillan, On radial limits and uniqueness of holomorphic functions, Math. Z. 92 (1966), 321-322. MR 0197736 (33:5899)
5.: I. I. Priwalow, Randeigenschaften analytischer Funktionen, Zweite, unter Redaktion von A. I. Markuschewitsch überarbeitete und ergänzte Auflage. Hochschulbücher für Mathematik, Bd. 25, VEB Deutscher Verlag der Wissenschaften, Berlin, 1956. MR 0083565 (18:727f)
6.: Walter Rudin, New constructions of functions holomorphic in the unit ball of ${\bf C}\sp n$ , CBMS Regional Conference Series in Mathematics, vol. 63, published for the Conference Board of the Mathematical Sciences, Washington, DC, by the Amer. Math. Soc., Providence, RI, 1986. MR 840468 (87f:32013)

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Additional Information:

Michael C. Fulkerson
Affiliation: Department of Mathematics, Mailstop 3368, Texas A&M University, College Station, Texas 77843
Address at time of publication: Department of Mathematics and Statistics, University of Central Oklahoma, Edmond, Oklahoma 73034
Email: mfulkerson@uco.edu

DOI: 10.1090/S0002-9939-09-10034-5
PII: S 0002-9939(09)10034-5
Received by editor(s): December 23, 2008
Posted: June 15, 2009
Additional Notes: This paper is based on part of the author's 2008 Ph.D. dissertation at Texas A&M University under the direction of Harold P. Boas.
Communicated by: Mei-Chi Shaw
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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