On the spectral Nevanlinna-Pick problem

• Autorzy: Constantin Costara
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 32F45: Invariant metrics and pseudodistances
• 30E05: Moment problems, interpolation problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 170
• Numer: 1
• Strony: 23-55

Daty

wydano

2005

Twórcy

autor

Constantin Costara

• Département de mathématiques et de statistique, Université Laval, Québec (QC) G1K 7P4, Canada

Identyfikatory

DOI

10.4064/sm170-1-2