We give several characterizations of the symmetrized n-disc Gₙ which generalize to the case n ≥ 3 the characterizations of the symmetrized bidisc that were used in order to solve the two-point spectral Nevanlinna-Pick problem in ℳ ₂(ℂ). Using these characterizations of the symmetrized n-disc, which give necessary and sufficient conditions for an element to belong to Gₙ, we obtain necessary conditions of interpolation for the general spectral Nevanlinna-Pick problem. They also allow us to give a method to construct analytic functions from the open unit disc of ℂ into Gₙ and to obtain some of the complex geodesics on Gₙ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-1-2,
author = {Constantin Costara},
title = {On the spectral Nevanlinna-Pick problem},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {23-55},
zbl = {1074.30035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-1-2}
}
Constantin Costara. On the spectral Nevanlinna-Pick problem. Studia Mathematica, Tome 166 (2005) pp. 23-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-1-2/