Correspondence between spirallike functions and starlike functions

Yong Chan Kim, Toshiyuki Sugawa

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Let λ be a real number with -π/2 < λ < π/2. In order to study λ-spirallike functions, it is natural to measure the angle according to λ-spirals. Thus we are led to the notion of λ-argument. This fits well the classical correspondence between λ-spirallike functions and starlike functions. Using this idea, we extend deep results of Pommerenke and Sheil-Small on starlike functions to spirallike functions. As an application, we solved a problem given by Hansen in 6.

Original languageEnglish
Pages (from-to)322-331
Number of pages10
JournalMathematische Nachrichten
Volume285
Issue number2-3
DOIs
Publication statusPublished - 2012 Feb 1

Keywords

  • Hardy space
  • Logarithmic spiral
  • Spirallike (spiral-like) function
  • Starlike function

ASJC Scopus subject areas

  • Mathematics(all)

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