ON MEROMORPHIC TYPICALLY-REAL FUNCTIONS,

Abstract

Let TM denote the class of funtions f(z) which are typically-real and meromorphic in the complex plane with slits on the real axis, analytic at z = 0, and normalized by f(0) = 0, f sub 1 (0) = 1. Characterizations of this class and a related class of functions are obtained as Stieltjes transforms and as bounded real J-fractions. From these representations, the exact regions of variability of functions in TM and of their first derivatives are derived. Finally, sharp regions of univalence of certain subclasses of TM are given. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1963
Accession Number
AD0430768

Entities

People

  • E. P. Merkes

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Data Mining and Knowledge Discovery.
  • Optical Physics and Photonics.