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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Unimodular functions and interpolating Blaschke products


Author: Geir Arne Hjelle
Journal: Proc. Amer. Math. Soc. 134 (2006), 207-214
MSC (2000): Primary 30D50, 30E10
Published electronically: June 2, 2005
MathSciNet review: 2170560
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Abstract: The result by Bourgain that every unimodular function $\psi$ on the unit circle can be factored as $\psi = e^{i \tilde v} B_1 \overline B_2$ with $B_1$ and $B_2$ Blaschke products can be improved. We show that the same result holds with $B_1$ and $B_2$ interpolating Blaschke products. This will at the same time be a refinement of Jones's result that every unimodular function can be approximated in the $H^\infty$-norm by a ratio of interpolating Blaschke products.


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Additional Information

Geir Arne Hjelle
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Email: hjelle@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07968-2
PII: S 0002-9939(05)07968-2
Received by editor(s): April 8, 2004
Received by editor(s) in revised form: August 25, 2004
Published electronically: June 2, 2005
Additional Notes: Research supported by grants from the Research Council of Norway, project #155060, and the Norwegian University of Science and Technology
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.