Univalent harmonic functions-Reference-Cited by-同舟云学术

Univalent harmonic functions

Published:1987 Issue:1 Volume:299 Page:1-31
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Hengartner W.,Schober G.

Abstract

Several families of complex-valued, univalent, harmonic functions are studied from the point of view of geometric function theory. One class consists of mappings of a simply-connected domain onto an infinite horizontal strip with a normalization at the origin. Extreme points and support points are determined, as well as sharp estimates for Fourier coefficients and distortion theorems. Next, mappings in | z | > 1 \left | z \right | > 1 are considered that leave infinity fixed. Some coefficient estimates, distortion theorems, and covering properties are obtained. For such mappings with real boundary values, many extremal problems are solved explicitly.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1987-299-01/S0002-9947-1987-0869396-9/S0002-9947-1987-0869396-9.pdf

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