On Lempert Functions in C
نویسنده
چکیده
We give a characterization of all cartesian products D1×D2 ⊂ C for which the Lempert function and the injective Lempert function coincide. In particular, we show that there exist domains in C for which they are different.
منابع مشابه
Lipschitzness of the Lempert and Green Functions
Necessary and sufficient conditions for Lipschitzness of the Lempert and Green functions are found in terms of their boundary behaviors.
متن کاملUpper Bound for the Lempert Function of Smooth Domains
An upper estimate for the Lempert function of any C-smooth bounded domain in C is found in terms of the boundary distance.
متن کاملNonisotropically Balanced Domains, Lempert Function Estimates, and the Spectral Nevanlinna-pick Problem
We introduce the notion of a Λ-nonisotropically balanced domain and show that the symmetrized polydisc in Cn, n ≥ 2, is an example of such a domain. Given a Λ-nonisotropically balanced domain Ω, we derive effective estimates from above and from below for the Lempert function κ̃Ω at (0, z) ∈ Ω × Ω. We use these estimates to derive certain conditions for realising a two-point Nevanlinna-Pick inter...
متن کامل