A counterexample to the $\varGamma $-interpolation conjecture
Volume 114 / 2015
Annales Polonici Mathematici 114 (2015), 115-121
MSC: Primary 47A56; Secondary 30E05.
DOI: 10.4064/ap114-2-2
Abstract
Agler, Lykova and Young introduced a sequence $C_\nu $, where $\nu \geq 0$, of necessary conditions for the solvability of the finite interpolation problem for analytic functions from the open unit disc $\mathbb D$ into the symmetrized bidisc $\varGamma $. They conjectured that condition $C_{n-2}$ is necessary and sufficient for the solvability of an $n$-point interpolation problem. The aim of this article is to give a counterexample to that conjecture.
