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Blaschke product
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(Definition)
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This product converges uniformly on compact subsets of the unit disc, and thus  is a holomorhic function on the unit disc. Further it is the function on the disc that has zeros exactly at  . And finally for  in the unit disc,
 .
Definition 2 Sometimes
 is called the Blaschke factor.
With this definition, the Blascke product becomes
 .
- 1
- John B. Conway. Functions of One Complex Variable I. Springer-Verlag, New York, New York, 1978.
- 2
- Steven G. Krantz. Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992.
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"Blaschke product" is owned by jirka.
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(view preamble)
| Also defines: |
Blascke factor |
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Cross-references: factor, disc, function, unit disc, compact subsets, converges uniformly, product, complex numbers, sequence
There is 1 reference to this entry.
This is version 5 of Blaschke product, born on 2004-04-22, modified 2005-12-07.
Object id is 5795, canonical name is BlaschkeProduct.
Accessed 3556 times total.
Classification:
| AMS MSC: | 30C45 (Functions of a complex variable :: Geometric function theory :: Special classes of univalent and multivalent functions ) |
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Pending Errata and Addenda
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