Computational Methods and Function Theory 7 (2007), No. 1, 33--41
Copyright Heldermann Verlag 2007
Prashant Batra
batra@tuhh.de , Institute for Computer Technology, Hamburg University of Technology, 21071 Hamburg, Germany.
Gol'dberg considered the class of functions analytic in the unit disc with unequal positive numbers of zeros and ones there. The maximum modulus of zero- and one-places in this class is non-trivially bounded from below by the universal constant A2. This constant determines a fundamental limit of controller design in engineering, and has applications when estimating covering regions for composites of fixed point free functions with schlicht functions. The lower bound for A2 is improved in this note by considering simultaneously the extremal functions f and 1-f together with their reciprocals.
Keywords: Gol'dberg's second constant, Schottky's Theorem, Borel-Hadamard inequalities, value distribution, holomorphic functions.
MSC 2000: 30C15, 93D15.
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