Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Proper holomorphic mappings of the spectral unit ball

Author(s): Wlodzimierz Zwonek
Journal: Proc. Amer. Math. Soc. 136 (2008), 2869-2874.
MSC (2000): Primary 32H35; Secondary 15A18, 32C25, 47N99
Posted: March 28, 2008
MathSciNet review: 2399052
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We prove an Alexander type theorem for the spectral unit ball $ \Omega _{n}$ showing that there are no non-trivial proper holomorphic mappings in $ \Omega _{n}$, $ n\geq 2$.

References:

[Ale 1977]
H. Alexander, Proper holomorphic mappings in $ \mathbb{C}\sp{n}$, Indiana Univ. Math. J. 26 (1977), 137-146. MR 0422699 (54:10685)

[Chi 1989]
E. Chirka, Complex Analytic Sets, Kluwer, 1989. MR 1111477 (92b:32016)

[Edi-Zwo 2005]
A. Edigarian, W. Zwonek, Geometry of the symmetrized polydisc, Arch. Math. (Basel) 84 (2005), 364-374. MR 2135687 (2006b:32020)

[Loj 1991]
S. Łojasiewicz, Introduction to Complex Analytic Geometry. Translated from the Polish by Maciej Klimek, Birkhäuser Verlag, Basel, 1991. MR 1131081 (92g:32002)

[Nik-Tho-Zwo 2007]
N. Nikolov, P. J. Thomas, W. Zwonek, Discontinuity of the Lempert function and the Kobayashi-Royden metric of the spectral ball, preprint.

[Ran-Whi 1991]
T. J. Ransford, M. C. White, Holomorphic self-maps of the spectral unit ball, Bull. London Math. Soc. 23 (1991), 256-262. MR 1123334 (92g:32049)

[Ros 2003]
J. Rostand, On the automorphisms of the spectral unit ball, Studia Math. 155 (2003), 207-230. MR 1961225 (2003m:32018)

[Rud 1980]
W. Rudin, Function theory in the unit ball of $ C\sp{n}$, Grundlehren der Mathematischen Wissenschaften 241, Springer-Verlag, New York-Berlin, 1980. MR 601594 (82i:32002)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32H35, 15A18, 32C25, 47N99

Retrieve articles in all Journals with MSC (2000): 32H35, 15A18, 32C25, 47N99

Additional Information:

Wlodzimierz Zwonek
Affiliation: Instytut Matematyki, Uniwersytet Jagiellonski, Reymonta 4, 30-059 Kraków, Poland
Email: Wlodzimierz.Zwonek@im.uj.edu.pl

DOI: 10.1090/S0002-9939-08-09512-9
PII: S 0002-9939(08)09512-9
Keywords: Spectral unit ball, proper holomorphic mappings, symmetrized polydisc
Received by editor(s): April 5, 2007
Posted: March 28, 2008
Additional Notes: This research was partially supported by Research Grant No. 1 PO3A 005 28 of the Polish Ministry of Science and Higher Education.
Communicated by: Mei-Chi Shaw
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia