Blaschke representation of functions on the circle

Wegert, Elias; von Wolfersdorf, Lothar

doi:10.1090/S0002-9939-07-08936-8

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 $\|f\|_\infty <1$.

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