Mathematics – Complex Variables
Scientific paper
2006-01-06
Mathematics
Complex Variables
12 pages. Added clarifications to Thm.1.8; added the important remark (Rmrk.1.3): the "only if" part of Thm.1.8 is a special c
Scientific paper
We introduce the notion of a \lambda-nonisotropically balanced domain and show that the symmetrized polydisc in C^n, n \geq 2, is an example of such a domain. Given a \lambda-nonisotropically balanced domain \Omega, we derive effective estimates from above and from below for the Lempert function at (0,z)\in\Omega\times\Omega. We use these estimates to derive certain conditions for realising a two-point Nevanlinna-Pick interpolation in the symmetrized polydisc. Applying the ideas used in the derivation of our Lempert function estimates to the so-called spectral unit ball \Omega_n, we deduce: a) a formula for the Lempert function at (0,W)\in\Omega_n\times\Omega_n; and b) a necessary and sufficient condition for realising a two-point Nevanlinna- Pick interpolation in the spectral unit ball.
No associations
LandOfFree
Nonisotropically balanced domains, Lempert function estimates, and the spectral Nevanlinna-Pick problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nonisotropically balanced domains, Lempert function estimates, and the spectral Nevanlinna-Pick problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonisotropically balanced domains, Lempert function estimates, and the spectral Nevanlinna-Pick problem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-110441