|
|
|
|
factorization theorem for  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 \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.
- 1
- John B. Conway. Functions of One Complex Variable II. Springer-Verlag, New York, New York, 1995.
|
"factorization theorem for  functions" is owned by .
|
|
(view preamble | get metadata)
Cross-references: function, conversely, outer function, inner function, unit disc, analytic functions, bounded
There are 2 references to this entry.
This is version 1 of factorization theorem for  functions, born on 2005-12-07.
Object id is 7523, canonical name is FactorizationTheoremForHinftyFunctions.
Accessed 1853 times total.
Classification:
| AMS MSC: | 30H05 (Functions of a complex variable :: Spaces and algebras of analytic functions) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
