Accession Number:

AD0256016

Title:

GRUNSKY INEQUALITIES AND COEFFICIENTS OF BOUNDED SCHLICHT FUNCTIONS

Descriptive Note:

Corporate Author:

HARVARD UNIV CAMBRIDGE MASS

Personal Author(s):

Report Date:

1961-04-01

Pagination or Media Count:

1.0

Abstract:

Let D be a plane finitely connected domain whose boundaries are closed Jordan curves C sub nu and let fz be a regular analytic function in D whose coefficients in power series expansion about a point zeta epsilon D are b sub nu. Grunsky had given a set of necessary and sufficient conditions, depending upon b sub nu, so that fz may be extended as a schlicht function in D. In the present report, Grunskys conditions have been extended to the case when fz has the additional restriction of being bounded, i.e., fz less than 1, z epsilon D. These conditions have then been used to get distortion theorems and coefficient inequalities for bounded schlicht functions in z less than 1 and in z greater than 1. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE