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THE SEMIADDICTION OF CONTINUOUS ANALYTIC CAPACITY AND THE INNER BOUNDARY CONJECTURE.
- Source :
- American Journal of Mathematics; Jun2004, Vol. 126 Issue 3, p523-567, 43p
- Publication Year :
- 2004
-
Abstract
- Let α(E) be the continuous analytic capacity of a compact set E ⊂ C. In this paper we obtain a characterization of α in terms of curvature of measures with zero linear density, and we deduce that α is countably semiadditive. This result has important consequences for the theory of uniform rational approximation on compact sets. In particular, it implies the so-called inner boundary conjecture. [ABSTRACT FROM AUTHOR]
- Subjects :
- MATHEMATICAL analysis
APPROXIMATION theory
ALGEBRA
POLYNOMIALS
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00029327
- Volume :
- 126
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- American Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 13673126
- Full Text :
- https://doi.org/10.1353/ajm.2004.0021