# name
Free interpolation by nonvanishing analytic functions

# metadata.dc.description.abstract[].value
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.

# metadata.dc.relation.ispartof[].value
Transactions of the American Mathematical Society, 2007, vol. 359, num. 9, p. 4449-4465

# metadata.dc.rights[].value
(c) American Mathematical Society (AMS), 2007

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Free interpolation by nonvanishing analytic functions