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Blaschke representation of functions on the circle
Author(s):
Elias
Wegert;
Lothar
von Wolfersdorf
Journal:
Proc. Amer. Math. Soc.
136
(2008),
161-170.
MSC (2000):
Primary 30E25;
Secondary 30D50, 81U40
Posted:
September 25, 2007
MathSciNet review:
2350401
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Abstract:
We prove that every unimodularly bounded measurable function on the complex unit circle admits a representation where  and  extend holomorphically into the interior and the exterior of the circle, respectively,  vanishes at infinity, and both functions are unimodularly bounded. The representation is unique if  .
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Additional Information:
Elias
Wegert
Affiliation:
Institute of Applied Analysis, TU Bergakademie Freiberg, 09596 Freiberg, Germany
Email:
wegert@math.tu-freiberg.de
Lothar
von Wolfersdorf
Affiliation:
Institute of Applied Analysis, TU Bergakademie Freiberg, 09596 Freiberg, Germany
Email:
wolfersd@math.tu-freiberg.de
DOI:
10.1090/S0002-9939-07-08936-8
PII:
S 0002-9939(07)08936-8
Received by editor(s):
June 26, 2006
Received by editor(s) in revised form:
September 22, 2006
Posted:
September 25, 2007
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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