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factorization theorem for $H^\infty$ functions (Theorem)

Let $ H^\infty$ denote the bounded analytic functions on the unit disc.

Theorem 1   Every $ f \in H^\infty$ can be written as
$\displaystyle f(z) = \alpha I(z) F(z)$    

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.

Bibliography

1
John B. Conway. Functions of One Complex Variable II. Springer-Verlag, New York, New York, 1995.



"factorization theorem for $H^\infty$ functions" is owned by jirka.
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See Also: inner function
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Cross-references: function, outer function, inner function, unit disc, analytic functions, bounded
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This is version 1 of factorization theorem for $H^\infty$ functions, born on 2005-12-07.
Object id is 7523, canonical name is FactorizationTheoremForHinftyFunctions.
Accessed 1352 times total.

Classification:
AMS MSC: 30H05 (Functions of a complex variable :: Spaces and algebras of analytic functions)
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