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Radial limits of interpolating Blaschke products

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Abstract.

It is shown that if (λ n ) is a sequence of distinct points on the unit circle, then, for a sequence (a n ) of points in the closed unit disk, there exists an interpolating Blaschke product B with B*(λ n )=a n for all n if and only if (a n ) is bounded away from zero. This complements results of Cargo, Carroll, Colwell, Belna and Piranian on prescribing radial limits for Blaschke products.

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Authors and Affiliations

  1. Department of Mathematics, Bucknell University, PA, 17837, Lewisburg, USA

    Pamela Gorkin

  2. Département de Mathématiques, Université de Metz, Ile du Saulcy, F-57045, Metz, France

    Raymond Mortini

Authors
  1. Pamela Gorkin
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  2. Raymond Mortini
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Correspondence to Raymond Mortini.

Additional information

Mathematics Subject Classification (2000): 30D50

Revised version: 1 June 2004

Acknowledgment The authors thank the Mathematisches Forschungsinstitut Oberwolfach for the support and for the kind hospitality they always receive. The work presented here is part of their 2002–2004 project “Inner functions”. The first author also thanks Universität Bern where she spent her sabbatical, as well as Université de Metz, where she was “professeur invité” for one month. The second author presented this work in May 2004 at the fourth congress of the European network “Analysis and Operators” in Dalfsen, the Netherlands. He gratefully acknowledges the support he received from the European community’s human potential program, contract HPRN-CT-2000-00116.

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Gorkin, P., Mortini, R. Radial limits of interpolating Blaschke products. Math. Ann. 331, 417–444 (2005). https://doi.org/10.1007/s00208-004-0588-0

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