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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Univalent functions in $ H\cdot \overline H(D)$


Authors: Z. Abdulhadi and D. Bshouty
Journal: Trans. Amer. Math. Soc. 305 (1988), 841-849
MSC: Primary 30C60
DOI: https://doi.org/10.1090/S0002-9947-1988-0924779-4
MathSciNet review: 924779
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Abstract: Functions in $ H \cdot \overline H (D)$ are sense-preserving of the form $ f = h \cdot \overline g $ where $ h$ and $ g$ are in $ H(D)$. Such functions are solutions of an elliptic nonlinear P.D.E. that is studied in detail especially for its univalent solutions.


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

  • [1] G. Choquet, Sur un type de transformation analytique généralisant la réprésentation conforme et définie au moven de fonction harmonique, Bull. Sci. Math. 2 (1945), 156-165. MR 0016973 (8:93a)
  • [2] J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I 9 (1984), 3-25. MR 752388 (85i:30014)
  • [3] W. Hengartner and G. Schober, Univalent harmonic functions, Trans. Amer. Math. Soc. 299 (1987), 1-31. MR 869396 (88e:30030)
  • [4] -, Harmonic mappings with given dilatation, J. London Math. Soc. 33 (1986), 473-483. MR 850963 (87j:30037)

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DOI: https://doi.org/10.1090/S0002-9947-1988-0924779-4
Article copyright: © Copyright 1988 American Mathematical Society

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