Aytuna, Aydın and Zakharyuta, Vyacheslav (2008) On lelongbremermann lemma. Proceedings of the American Mathematical Society, 136 (5). pp. 17331742. ISSN 10886826 (e) ISSN 00029939 (p)
This is the latest version of this item.
PDF
aytzahcor.pdf
Download (198kB)
aytzahcor.pdf
Download (198kB)
Official URL: http://dx.doi.org/10.1090/S0002993908091661
Abstract
The main theorem of this note is the following refinement of the wellknown LelongBremermann Lemma:
Let u be a continuous plurisubharmonic function on a Stein manifold. of dimension n. Then there exists an integer m <= 2n + 1, natural numbers p(s), and analytic mappings G(s) = (g(j)((s))): Omega > Cm, s = 1, 2,..., such that the sequence of functions
u(s) (z) = 1/p(s) max (ln vertical bar g(j)((s)) (z)vertical bar : j = 1,..., m
converges to u uniformly on each compact subset of Omega.
In the case when Omega is a domain in the complex plane, it is shown that one can take m = 2 in the theorem above (Section 3); on the other hand, for ncircular plurisubharmonic functions in Cn the statement of this theorem is true with m = n + 1 (Section 4). The last section contains some remarks and open questions.
Item Type:  Article 

Uncontrolled Keywords:  Plurisubharmonic functions, LelongBremermann Lemma 
Subjects:  Q Science > QA Mathematics > QA299.6433 Analysis 
Divisions:  Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences 
Depositing User:  Vyacheslav Zakharyuta 
Date Deposited:  16 Dec 2008 11:11 
Last Modified:  26 Apr 2022 08:26 
URI:  https://research.sabanciuniv.edu/id/eprint/10998 
Available Versions of this Item

On LelongBremermann Lemma. (deposited 18 Nov 2007 14:32)
 On lelongbremermann lemma. (deposited 16 Dec 2008 11:11) [Currently Displayed]