On the spectral Nevanlinna-Pick problem

Constantin Costara. "On the spectral Nevanlinna-Pick problem." Studia Mathematica 170.1 (2005): 23-55. <http://eudml.org/doc/285169>.

@article{ConstantinCostara2005,
abstract = {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.},
author = {Constantin Costara},
journal = {Studia Mathematica},
keywords = {Nevanlinna-Pick problem; spectral; matrix},
language = {eng},
number = {1},
pages = {23-55},
title = {On the spectral Nevanlinna-Pick problem},
url = {http://eudml.org/doc/285169},
volume = {170},
year = {2005},
}

TY - JOUR
AU - Constantin Costara
TI - On the spectral Nevanlinna-Pick problem
JO - Studia Mathematica
PY - 2005
VL - 170
IS - 1
SP - 23
EP - 55
AB - 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.
LA - eng
KW - Nevanlinna-Pick problem; spectral; matrix
UR - http://eudml.org/doc/285169
ER -