Translator Disclaimer
April 2009 Convergence and multiplicities for the Lempert function
Pascal J. Thomas, Nguyen Van Trao
Author Affiliations +
Ark. Mat. 47(1): 183-204 (April 2009). DOI: 10.1007/s11512-008-0092-y


Given a domain Ω⊂ℂn, the Lempert function is a functional on the space $\text{Hol}(\mathbb{D},\Omega)$ of analytic disks with values in Ω, depending on a set of poles in Ω. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the local indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.


Download Citation

Pascal J. Thomas. Nguyen Van Trao. "Convergence and multiplicities for the Lempert function." Ark. Mat. 47 (1) 183 - 204, April 2009.


Received: 29 January 2007; Revised: 25 March 2008; Published: April 2009
First available in Project Euclid: 31 January 2017

zbMATH: 1181.32018
MathSciNet: MR2480920
Digital Object Identifier: 10.1007/s11512-008-0092-y

Rights: 2008 © Institut Mittag-Leffler


Vol.47 • No. 1 • April 2009
Back to Top