GRUNSKY INEQUALITIES AND COEFFICIENTS OF BOUNDED SCHLICHT FUNCTIONS
Abstract
Let D be a plane finitely connected domain whose boundaries are closed Jordan curves C sub nu and let f(z) 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 f(z) may be extended as a schlicht function in D. In the present report, Grunsky's conditions have been extended to the case when f(z) has the additional restriction of being bounded, i.e., /f(z)/ 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1961
- Accession Number
- AD0256016
Entities
People
- Vikramaditya Singh
Organizations
- Harvard University