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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Univalent functions which map onto regions of given transfinite diameter


Authors: P. L. Duren and M. M. Schiffer
Journal: Trans. Amer. Math. Soc. 323 (1991), 413-428
MSC: Primary 30C70; Secondary 30C50, 30C85
MathSciNet review: 979964
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Abstract | References | Similar Articles | Additional Information

Abstract: By a variational method, the sharp upper bound is obtained for the second coefficients of normalized univalent functions which map the unit disk onto regions of prescribed transfinite diameter, or logarithmic capacity.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-0979964-2
PII: S 0002-9947(1991)0979964-2
Keywords: Univalent functions, second coefficient, extremal problems, variational methods, quadratic differentials, transfinite diameter, logarithmic capacity, elliptic integrals
Article copyright: © Copyright 1991 American Mathematical Society