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Journal of the London Mathematical Society 2005 72(1):151-168; doi:10.1112/S0024610705006411
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© The London Mathematical Society

Value Distribution of Interpolating Blaschke Products

Pamela Gorkin and Raymond Mortini

Department of Mathematics, Bucknell University Lewisburg, PA 17837, USA pgorkin{at}bucknell.edu
Département de Mathématiques, Université de Metz Ile du Saulcy, F–57045 Metz, France mortini{at}poncelet.univ-metz.fr

Received 19 January 2004.

A Blaschke product B with zero-sequence (an) is called almost interpolating if the inequality lim infn(1 – |an|2)|B'(an)| ≥ {delta} > 0 holds. The sets U for which there exists a Blaschke product B such that (a – B)/(1 – aB) is almost interpolating if and only if a isin U are studied. Examples of such sets include open sets, containing the origin, and whose complement is the closure of an arbitrary set of concentric open arcs around the origin or open sets whose complement is of zero logarithmic capacity. Results on the range of interpolating Blaschke product s on the set of trivial points in the spectrum of H{infty} are deduced.


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