Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/97263
 Title: Free interpolation by nonvanishing analytic functions Author: Dyakonov, Konstantin M.Nicolau, Artur Keywords: Àlgebres de BanachÀlgebres topològiquesAnàlisi funcionalFuncions enteresFuncions meromorfesBanach algebrasTopological algebrasFunctional analysisEntire functionsMeromorphic functions Issue Date: Sep-2007 Publisher: American Mathematical Society (AMS) Abstract: We 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. Note: Reproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9947-07-04186-4 It is part of: Transactions of the American Mathematical Society, 2007, vol. 359, num. 9, p. 4449-4465 Related resource: http://dx.doi.org/10.1090/S0002-9947-07-04186-4 URI: http://hdl.handle.net/2445/97263 ISSN: 0002-9947 Appears in Collections: Articles publicats en revistes (Matemàtiques i Informàtica)

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