Dyakonov, Konstantin M.Nicolau, Artur2016-04-122016-04-122007-090002-9947https://hdl.handle.net/2445/97263We are concerned with interpolation problems in $ H^\infty$ where the values prescribed and the function to be found are both zero-free. More precisely, given a sequence $ \{z_j\}$ in the unit disk, we ask whether there exists a nontrivial minorant $ \{\varepsilon_j\}$ (i.e., a sequence of positive numbers bounded by 1 and tending to 0) such that every interpolation problem $ f(z_j)=a_j$ has a nonvanishing solution $ f\in H^\infty$ whenever $ 1\ge\vert a_j\vert\ge\varepsilon_j$ for all $ j$. The sequences $ \{z_j\}$ with this property are completely characterized. Namely, we identify them as 'thin' sequences, a class that arose earlier in Wolff's work on free interpolation in $ H^\infty\cap$ VMO.17 p.application/pdfeng(c) American Mathematical Society (AMS), 2007Àlgebres de BanachÀlgebres topològiquesAnàlisi funcionalFuncions enteresFuncions meromorfesBanach algebrasTopological algebrasFunctional analysisEntire functionsMeromorphic functionsinfo:eu-repo/semantics/article5824522016-04-12info:eu-repo/semantics/openAccess