Interpolating Blaschke products and angular derivatives
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- by Eva A. Gallardo-Gutiérrez and Pamela Gorkin PDF
- Trans. Amer. Math. Soc. 364 (2012), 2319-2337 Request permission
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 \[ H^\infty [\overline {b}: b~\mbox {has finite angular derivative everywhere}].\] 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.References
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Additional Information
- Eva A. Gallardo-Gutiérrez
- Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid Plaza de Ciencias 3 28040, Madrid, Spain
- MR Author ID: 680697
- Email: eva.gallardo@mat.ucm.es
- Pamela Gorkin
- Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvannia 17837
- MR Author ID: 75530
- Email: pgorkin@bucknell.edu
- Received by editor(s): February 18, 2010
- Published electronically: January 3, 2012
- Additional Notes: The first author was partially supported by the grant MTM2010-16679 and the Gobierno de Aragón research group Análisis Matemático y Aplicaciones, ref. DGA E-64.
The second author wishes to thank the University of Zaragoza for the support provided by a grant from the research institute IUMA and for its hospitality during the fall of 2009. - © Copyright 2012 American Mathematical Society
- 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
- MathSciNet review: 2888208