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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Integral representations of univalent functions and singular measures


Author: Robert J. Bass
Journal: Proc. Amer. Math. Soc. 110 (1990), 731-739
MSC: Primary 30E20; Secondary 30C55
MathSciNet review: 1028039
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Abstract: In [5], T. MacGregor showed that not every univalent function has a proposed integral representation with respect to Borel measures on the unit circle. In this paper, we study the decomposition of measures which do give rise to univalent functions. The main results show that no measure with a continuous singular component can ever be associated with a univalent function.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1028039-X
PII: S 0002-9939(1990)1028039-X
Keywords: Univalent functions, integral representations, close-to-convex functions
Article copyright: © Copyright 1990 American Mathematical Society