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Blaschke representation of functions on the circle

Author(s): Elias Wegert; Lothar von Wolfersdorf
Journal: Proc. Amer. Math. Soc. 136 (2008), 161-170.
MSC (2000): Primary 30E25; Secondary 30D50, 81U40
Posted: September 25, 2007
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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: 10.1090/S0002-9939-07-08936-8
PII: S 0002-9939(07)08936-8
Received by editor(s): June 26, 2006
Received by editor(s) in revised form: September 22, 2006
Posted: September 25, 2007
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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