Accession Number : AD0621641

Title :   BOUNDED APPROXIMATION BY POLYNOMIALS,

Corporate Author : ILLINOIS UNIV URBANA

Personal Author(s) : Rubel,L. A. ; Shields,A. L.

Report Date : 28 SEP 1963

Pagination or Media Count : 21

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-.

Descriptors :   (*FUNCTIONAL ANALYSIS, POLYNOMIALS), (*POLYNOMIALS, FUNCTIONAL ANALYSIS), SEQUENCES(MATHEMATICS), COMPLEX VARIABLES, NUMERICAL ANALYSIS, THEOREMS

Distribution Statement : APPROVED FOR PUBLIC RELEASE