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-.

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE