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  4. On small circles containing zeros and ones of analytic functions
 
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On small circles containing zeros and ones of analytic functions

Publikationstyp
Journal Article
Date Issued
2004
Sprache
English
Author(s)
Batra, Prashant  orcid-logo
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/8919
Journal
Complex variables  
Volume
49
Issue
11
Start Page
787
End Page
791
Citation
Complex Variables, Theory and Application: An International Journal 49 (11): 787-791 (2006)
Publisher DOI
10.1080/02781070412331298615
Publisher
Taylor & Francis
Gol'dberg considered the class of functions with unequal positive numbers of zeros and ones inside the unit disc. The maximum modulus of zeros and ones in this class is bounded from below by a universal constant. This constant determines the limits of certain controller designs as well as covering regions of certain composites with schlicht functions. Considering lower bounds in a zero-free region of the extremal function the best known estimates of this constant are improved.
Subjects
Goldberg's second constant
Schottky's theorem
value distribution
DDC Class
510: Mathematik
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