Arkiv för Matematik

  • Ark. Mat.
  • Volume 47, Number 1 (2009), 183-204.

Convergence and multiplicities for the Lempert function

Pascal J. Thomas and Nguyen Van Trao

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Abstract

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.

Article information

Source
Ark. Mat., Volume 47, Number 1 (2009), 183-204.

Dates
Received: 29 January 2007
Revised: 25 March 2008
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907068

Digital Object Identifier
doi:10.1007/s11512-008-0092-y

Mathematical Reviews number (MathSciNet)
MR2480920

Zentralblatt MATH identifier
1181.32018

Rights
2008 © Institut Mittag-Leffler

Citation

Thomas, Pascal J.; Trao, Nguyen Van. Convergence and multiplicities for the Lempert function. Ark. Mat. 47 (2009), no. 1, 183--204. doi:10.1007/s11512-008-0092-y. https://projecteuclid.org/euclid.afm/1485907068


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