Radial limits of interpolating Blaschke products

It is shown that if (_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*(_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.Mathematics Subject Classification (2000): 30D50Revised version: 1 June 2004Acknowledgment 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 communitys human potential program, contract HPRN-CT-2000-00116.