International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 641-647
doi:10.1155/S0161171281000471
On holomorphic functions with certain extremal properties of its absolute values
Dieter Schmersau
Mathematisches Institut der Freien Universität Berlin, FB 19, WE 1, Hüttenweg 9, Berlin 33 1000, Germany
Abstract
This paper is concerned with a special class of holomorphic functions with extremal properties of its absolute values on arbitrary closed line segments in the complex plane. The main result is a geometrical characterization of the functions z→eaz+b, z→(az+b)n and z→(az+b)α+iβ with a,b,∈ℂ, α,β∈ℝ, n∈ℤ.