factorization theorem for $H^\infty$ functionsFactorizationTheoremForHinftyFunctions2005-12-07 12:33:502005-12-07 12:33:50Theorem% this is the default PlanetMath preamble. as your knowledge
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\newtheorem*{rmk}{Remark}Let $H^\infty$ denote the bounded analytic functions on the unit disc.
\begin{thm}
Every $f \in H^\infty$ can be written as
\begin{equation*}
f(z) = \alpha I(z) F(z)
\end{equation*}
where $\lvert \alpha \rvert = 1$, $I$ is an inner function and $F$ is a bounded outer function. Conversely any function which can be so written is bounded.
\end{thm}
\begin{thebibliography}{9}
\bibitem{Conway:complexII}
John~B. Conway.
{\em \PMlinkescapetext{Functions of One Complex Variable II}}.
Springer-Verlag, New York, New York, 1995.
\end{thebibliography}