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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: 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 |
URI: | http://hdl.handle.net/2445/97263 |
Related resource: | http://dx.doi.org/10.1090/S0002-9947-07-04186-4 |
ISSN: | 0002-9947 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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