Accession Number : AD0662741

Title :   AN APPLICATION OF AN ESTIMATE OF THE RIEMANN MAPPING FUNCTION FOR CERTAIN STAR-SHAPED DOMAINS.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Cannon,John R.

Report Date : SEP 1967

Pagination or Media Count : 10

Abstract : Let D denote a simply connected domain contained in the simply connected star-shaped domain G. Let u denote a harmonic function in G which is bounded by M throughout G and by m , m < M, in D. For any compact set S in G, there exist explicitly defined constants K = K(M,G,D,S) and alpha = alpha(G,D,S), 0 < alpha < 1, such that the absolute value of u < K(m to the power alpha) throughout S. (Author)

Descriptors :   (*COMPLEX VARIABLES, MAPPING(TRANSFORMATIONS)), SET THEORY, POTENTIAL THEORY, FUNCTIONS(MATHEMATICS), ANALYTIC FUNCTIONS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE