A VARIATIONAL METHOD FOR FUNCTIONS SCHLICHT IN AN ANNULUS
Abstract
Consideration is given to the family of function f(z) regular analytic and schlicht in the annulus R and satisfying the following conditions: (1) f(z) maps R onto the unit disk minus some continuum G, and (2) G contains the origin. Extremal problems (maximum modulus on the inner boundary and maximum displacement on the outer boundary of R) are solved using a specific method of variation within the family. The variation leads from every given f(z) to a large set of comparison functions within the family. The use of the variational method is further illustrated in finding the maximum diameter of the continuum G for all functions in the family F.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 11, 1961
- Accession Number
- AD0265022
Entities
People
- M. Schiffer
- P.l. Duren
Organizations
- Stanford University