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Blaschke representation of functions on the circle


Authors: Elias Wegert and Lothar von Wolfersdorf
Journal: Proc. Amer. Math. Soc. 136 (2008), 161-170
MSC (2000): Primary 30E25; Secondary 30D50, 81U40
Published electronically: September 25, 2007
MathSciNet review: 2350401
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Abstract: We prove that every unimodularly bounded measurable function on the complex unit circle admits a representation

$\displaystyle f=\frac{f_++f_-}{1+\overline{f}_-f_+}, $

where $ f_+$ and $ f_-$ extend holomorphically into the interior and the exterior of the circle, respectively, $ f_-$ vanishes at infinity, and both functions are unimodularly bounded. The representation is unique if $ \Vert f\Vert _\infty<1$.


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Additional Information

Elias Wegert
Affiliation: Institute of Applied Analysis, TU Bergakademie Freiberg, 09596 Freiberg, Germany
Email: wegert@math.tu-freiberg.de

Lothar von Wolfersdorf
Affiliation: Institute of Applied Analysis, TU Bergakademie Freiberg, 09596 Freiberg, Germany
Email: wolfersd@math.tu-freiberg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08936-8
Received by editor(s): June 26, 2006
Received by editor(s) in revised form: September 22, 2006
Published electronically: September 25, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.