Unimodular functions and interpolating Blaschke products
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- by Geir Arne Hjelle PDF
- Proc. Amer. Math. Soc. 134 (2006), 207-214 Request permission
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.References
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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
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 207-214
- MSC (2000): Primary 30D50, 30E10
- DOI: https://doi.org/10.1090/S0002-9939-05-07968-2
- MathSciNet review: 2170560