Accession Number : AD0265022

Title :   A VARIATIONAL METHOD FOR FUNCTIONS SCHLICHT IN AN ANNULUS

Corporate Author : STANFORD UNIV CALIF APPLIED MATHEMATICS AND STATISTICS LABS

Personal Author(s) : DUREN,P.L. ; SCHIFFER,M.

Report Date : 11 SEP 1961

Pagination or Media Count : 1

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.

Descriptors :   *CALCULUS OF VARIATIONS, *CONFORMAL MAPPING, FUNCTIONS(MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE