BOUNDED APPROXIMATION BY POLYNOMIALS,
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-.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 28, 1963
- Accession Number
- AD0621641
Entities
People
- A. L. Shields
- L. A. Rubel
Organizations
- University of Illinois Urbana–Champaign