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VALUE DISTRIBUTION OF INTERPOLATING BLASCHKE PRODUCTS

Published online by Cambridge University Press:  20 July 2005

PAMELA GORKIN
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, [email protected]
RAYMOND MORTINI
Affiliation:
Département de Mathématiques, Université de Metz, Ile du Saulcy, F–57045 Metz, [email protected]
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Abstract

A Blaschke product $B$ with zero-sequence $(a_n)$ is called almost interpolating if the inequality $\liminf_n(1-|a_n|^2)|B'(a_n)|\geqslant \d>0$ holds. The sets $U$ for which there exists a Blaschke product $B$ such that $(a-B)/(1-\ov a B)$ is almost interpolating if and only if $a \in U$ 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.

Type
Notes and Papers
Copyright
The London Mathematical Society 2005

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Footnotes

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