Convergence and multiplicities for the Lempert function

Pascal J. Thomas Institut de Mathématiques de Toulouse, Université de Toulouse et CNRS (UMR 5219) Nguyen Van Trao Department of Mathematics, Dai Hoc Su Pham 1 (Pedagogical Institute of Hanoi)

TBD mathscidoc:1701.333144

Arkiv for Matematik, 47, (1), 183-204, 2007.1
Given a domain Ω⊂ℂ^{$n$}, 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.
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@inproceedings{pascal2007convergence,
  title={Convergence and multiplicities for the Lempert function},
  author={Pascal J. Thomas, and Nguyen Van Trao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203624506887953},
  booktitle={Arkiv for Matematik},
  volume={47},
  number={1},
  pages={183-204},
  year={2007},
}
Pascal J. Thomas, and Nguyen Van Trao. Convergence and multiplicities for the Lempert function. 2007. Vol. 47. In Arkiv for Matematik. pp.183-204. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203624506887953.
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