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Cluster sets of interpolating Blaschke products

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Abstract

We construct interpolating Balschke products whose radial cluster sets at a given point of the unit circle can be prescribed to be one of the following: the closed unit disk; an arbitrary closed arc on the unit circle; an arbitrary interval of the form [x, y], wherexy ≠ 0 and −1≤1x≤y≤1. We also show that there does not exist an interpolating Blaschke product having [0,y] or [x, 0] as a radial cluster set. On the other hand, there do exist finite products of interpolating Blaschke products that have [0, 1] as a radial cluster set.

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Authors and Affiliations

  1. Department of Mathematics, Bucknell University, 17837, Lewisburg, PA, 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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Additional information

Research supported by the RIP-program Oberwolfach, 2002/2003.

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Gorkin, P., Mortini, R. Cluster sets of interpolating Blaschke products. J. Anal. Math. 96, 369–395 (2005). https://doi.org/10.1007/BF02787836

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  • DOI: https://doi.org/10.1007/BF02787836

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