Accession Number : AD0267250

Title :   TRANSFINITE DIAMETER AND ANALYTIC CONTINUATION OF FUNCTIONS OF TWO COMPLEX VARIABLES

Corporate Author : STANFORD UNIV CALIF APPLIED MATHEMATICS AND STATISTICS LABS

Personal Author(s) : SCHIFFER,M. ; SICIAK,J.

Report Date : 16 OCT 1961

Pagination or Media Count : 1

Abstract : An e te sion to Polya's result to the theory of analytic functions in two (an more) complex vari ble is pr sented. n stimate for the singular set of a function in terms of the coefficients of a power series eleme t is given. Applications will be ade which throw a new light upon the geometry of domains in the complex z-plane whose boundary has a given transfinite diameter. Some asymptotic results whichALLOW THE C LCULATION OF THE TR NSFI I DI R OF A PLAN R DOMAIN BY MEANS OF THE KERNEL FUNCTION OF THIS DOMAIN IS OBTAINED. The definitions of a transfinite diameter of produc s s in he space of two complex variables as w ll as extension of these definitions in the case of more than two complex variables is discussed. (Author)

Descriptors :   *COMPLEX VARIABLES, *MATHEMATICAL ANALYSIS, COMBINATORIAL ANALYSIS, FUNCTIONS(MATHEMATICS), INTEGRAL EQUATIONS, MATRICES(MATHEMATICS), TOPOLOGY

Distribution Statement : APPROVED FOR PUBLIC RELEASE