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Title: Free interpolation by nonvanishing analytic functions
Author: Dyakonov, Konstantin M.
Nicolau, Artur
Keywords: Àlgebres de Banach
Àlgebres topològiques
Anàlisi funcional
Funcions enteres
Funcions meromorfes
Banach algebras
Topological algebras
Functional analysis
Entire functions
Meromorphic 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:
It is part of: Transactions of the American Mathematical Society, 2007, vol. 359, num. 9, p. 4449-4465
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ISSN: 0002-9947
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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