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A counterexample to the Γ-interpolation conjecture

Adama S. Kamara (2015)

Annales Polonici Mathematici

Agler, Lykova and Young introduced a sequence C ν , 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 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.

A Dichotomy Principle for Universal Series

V. Farmaki, V. Nestoridis (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

Applying results of the infinitary Ramsey theory, namely the dichotomy principle of Galvin-Prikry, we show that for every sequence ( α j ) j = 1 of scalars, there exists a subsequence ( α k j ) j = 1 such that either every subsequence of ( α k j ) j = 1 defines a universal series, or no subsequence of ( α k j ) j = 1 defines a universal series. In particular examples we decide which of the two cases holds.

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