Blaschke representation of functions on the circle
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- by Elias Wegert and Lothar von Wolfersdorf PDF
- Proc. Amer. Math. Soc. 136 (2008), 161-170 Request permission
Abstract:
We prove that every unimodularly bounded measurable function on the complex unit circle admits a representation \[ f=\frac {f_++f_-}{1+\overline {f}_-f_+}, \] 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 $\|f\|_\infty <1$.References
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Additional Information
- Elias Wegert
- Affiliation: Institute of Applied Analysis, TU Bergakademie Freiberg, 09596 Freiberg, Germany
- MR Author ID: 181195
- ORCID: 0000-0002-1183-9720
- 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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 161-170
- MSC (2000): Primary 30E25; Secondary 30D50, 81U40
- DOI: https://doi.org/10.1090/S0002-9939-07-08936-8
- MathSciNet review: 2350401