2006/09/18 by Pascal J. Thomas, Thomas, Pascal J., Nguyen Van Trao +1
Mathematics · #32U35 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Differential Equations Analysis #math.CV #msc:32U35
paper · pdf · doi:10.48550/arxiv.math/0609499
24 pages; many typos corrected thanks to the referee of Arkiv for Matematik
openalex publication_date 2006/09/18 · arxiv created 2008/03/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a domain Ω⊂ \mathbb C, the Lempert function is a functional on the space Hol (\D,Ω) 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's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the 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.