A convergence theorem for a method for simultaneous determination of all zeros of a polynomial.
Agler, Lykova and Young introduced a sequence , where ν ≥ 0, of necessary conditions for the solvability of the finite interpolation problem for analytic functions from the open unit disc into the symmetrized bidisc Γ. They conjectured that condition 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.
Applying results of the infinitary Ramsey theory, namely the dichotomy principle of Galvin-Prikry, we show that for every sequence of scalars, there exists a subsequence such that either every subsequence of defines a universal series, or no subsequence of defines a universal series. In particular examples we decide which of the two cases holds.