On holomorphic functions with certain extremal properties of its absolute values

Dieter Schmersau

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-7

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 → e a z + b , z → ( a z + b ) n and z → ( a z + b ) α + i β with a , b , ∈ ℂ , α , β ∈ ℝ , n ∈ ℤ .

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:825707

DOI: 10.1155/S0161171281000471

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