TRANSFINITE DIAMETER AND ANALYTIC CONTINUATION OF FUNCTIONS OF TWO COMPLEX VARIABLES
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 16, 1961
- Accession Number
- AD0267250
Entities
People
- J. Siciak
- M. Schiffer
Organizations
- Stanford University