On holomorphic functions with certain extremal properties of its absolute values

[摘要] 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 functionsz→eaz+b,z→(az+b)nandz→(az+b)α+iβwitha,b,∈ℂ,α,β∈ℝ,n∈ℤ.

[学科分类] 数学（综合）