Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Hausdorff dimension of Cantor sets and polynomial hulls

Author: Burglind Jöricke
Journal: Proc. Amer. Math. Soc. 134 (2006), 1347-1354
MSC (2000): Primary 32E20; Secondary 46J15, 46J20
Posted: October 7, 2005
MathSciNet review: 2199178
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give examples of Cantor sets in $\mathbb{C}^n$ of Hausdorff dimension 1 whose polynomial hulls have non-empty interior.

References

[A1] ALEXANDER H., Polynomial approximation and hulls in sets of finite linear measure in $\mathbb{C}^n$ , Amer. J. Math., 93 (1971), 65-74. MR 0284617 (44:1841)
[A2] ALEXANDER H., The polynomial hull of a set of finite linear measure in $\mathbb{C}^n$ , J. Analyse Math., 47 (1986), 238-242.MR 0874052 (88b:32038)
[DL] DINH T.-C. AND LAWRENCE M., Polynomial hulls and positive currents, Ann. Fac. Sci. Toulouse, 12 (2003), 317-334. MR 2030090 (2005b:32022)
[H] HENKIN G.M., Oral communication.
[J] JÖRICKE B., A Cantor set in the unit sphere in $\mathbb{C}^2$ with large polynomial hull, Mich. Math. J., 53 (2005), 189-207. MR 2125541
[R] RUDIN W., Function algebras, (Proc. Internat. Sympos., Tulane Univ., 1965), Scott, Foresman, Chicago, IL, 1966.
[Si] SIBONY N., Sur la frontière de Shilov des domaines de $\mathbb{C}^n$ , Math. Ann., 273 (1985), 115-121. MR 0814198 (87d:32029)
[S] STOLZENBERG G., Uniform approximation on smooth curves, Acta Math., 115 (1966), 185-198. MR 0192080 (33:307)
[V] VITUSHKIN A.G., On a problem of W. Rudin, Dokl. Akad. Nauk USSR, 213 (1973), 14-15, transl. in Soviet. Math. Dokl., 14 (1973), 1618-1619. MR 0333243 (48:11568)
[W] WERMER J., The hull of a curve in $\mathbb{C}^n$ , Ann. of Math., 68 (1958), 550-561. MR 0100102 (20:6536)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32E20, 46J15, 46J20

Retrieve articles in all journals with MSC (2000): 32E20, 46J15, 46J20

Additional Information

Burglind Jöricke
Affiliation: Department of Mathematics, Uppsala University, Box 480, S-751 06 Uppsala, Sweden
Email: joericke@math.uu.se

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08102-5
PII: S 0002-9939(05)08102-5
Keywords: Cantor sets, polynomial hulls, Hausdorff dimension.
Received by editor(s): November 25, 2004
Posted: October 7, 2005
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|