Interpolating Blaschke products and angular derivatives

Gallardo-Gutiérrez, Eva; Gorkin, Pamela

doi:10.1090/S0002-9947-2012-05535-8

Interpolating Blaschke products and angular derivatives

Authors: Eva A. Gallardo-Gutiérrez and Pamela Gorkin
Journal: Trans. Amer. Math. Soc. 364 (2012), 2319-2337
MSC (2010): Primary 46J15, 30J10; Secondary 30H10, 47B38
DOI: https://doi.org/10.1090/S0002-9947-2012-05535-8
Published electronically: January 3, 2012
MathSciNet review: 2888208
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Abstract: We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra

$\displaystyle H^\infty [\overline {b}: b~$ $\displaystyle \mbox {has finite angular derivative everywhere}].$

We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

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