# Accession Number:

## AD0621641

# Title:

## BOUNDED APPROXIMATION BY POLYNOMIALS,

# Descriptive Note:

# Corporate Author:

## ILLINOIS UNIV URBANA

# Personal Author(s):

# Report Date:

## 1963-09-28

# Pagination or Media Count:

## 21.0

# Abstract:

This paper presents a complete solution to the following problem if G is an arbitrary bounded open set in the complex plane, characterize those functions in G that can be obtained as the bounded pointwise limits of polynomials in G. Roughly speaking, the answer is that a function is such a limit if and only if it has a bounded analytic continuation throughout a certain bounded open set G that contains G. This set G is the inside of the outer boundary of G. More precisely, if G is a bounded open set and if H is the unbounded component of the complement of G- the closure of G, then G denotes the complement of H-.