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

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Analytic Functions
  • Boundaries
  • Coefficients
  • Complex Variables
  • Diameters
  • Functions (Mathematics)
  • Geometry
  • Kernel Functions
  • Mathematical Analysis
  • Mathematics
  • Power Series
  • Special Functions (Mathematics)

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Snow Cover Descriptors for Reptiles and Their Illustrations.
  • Theoretical Analysis.

Technology Areas

  • Space