Families of real and symmetric analytic functions
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- by Yusuf Abu-Muhanna and Thomas H. MacGregor PDF
- Trans. Amer. Math. Soc. 263 (1981), 59-74 Request permission
Abstract:
We introduce families of functions analytic in the unit disk and having rotational symmetries. The families include the $k$-fold symmetric univalent functions which have real coefficients. We relate the families to special classes of functions with a positive real part and then determine their extreme points. The case $k = 2$ corresponds to the odd functions which "preserve quadrants" and the extreme points of this set are characterized by having a radial limit which is real or imaginary almost everywhere. We also find estimates on the initial coefficients of functions in the families.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 263 (1981), 59-74
- MSC: Primary 30C45; Secondary 30C50
- DOI: https://doi.org/10.1090/S0002-9947-1981-0590411-9
- MathSciNet review: 590411