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Interpolating Blaschke products and angular derivatives

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Gallardo Gutiérrez, Eva A. (2012) Interpolating Blaschke products and angular derivatives. Transactions of the American Mathematical Society, 364 (5). pp. 2319-2337. ISSN 0002-9947

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Official URL: http://www.ams.org/journals/tran/2012-364-05/S0002-9947-2012-05535-8/S0002-9947-2012-05535-8.pdf


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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

H-infinity[(b) over bar : b 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.


Item Type:Article
Uncontrolled Keywords:Blaschke product; interpolating Blaschke product; angular derivative
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:20975
Deposited On:22 Apr 2013 11:42
Last Modified:10 Aug 2018 08:53

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