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Interpolation problems on the spectrum of H ∞

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Abstract

We characterize those sequences (x n ) in the spectrum of H ∞ whose Nevanlinna–Pick interpolation problems admit thin Blaschke products as solutions. We also study under which conditions there is a Blaschke product B with prescribed zero-set distribution and solving problems of the form B(x) = f n (x) for every x ∈ P(x n ), where P(x n ) is the Gleason part associated with the point x n and where (f n ) is an arbitrary sequence of functions in the unit ball of H ∞. As a corollary we get a new characterization of Carleson–Newman Blaschke products in terms of bounded universal functions, a result first proved by Gallardo and Gorkin.

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  1. Département de Mathématiques et LMAM, Université Paul Verlaine, Ile du Saulcy, 57045, Metz, France

    Raymond Mortini

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Mortini, R. Interpolation problems on the spectrum of H ∞ . Monatsh Math 158, 81–95 (2009). https://doi.org/10.1007/s00605-008-0040-8

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