Abstract
In 1991, J. E. Thomson determined completely the structure of H2(μ), the closed subspace of L2(μ) that is spanned by the polynomials, whenever μ is a compactly supported measure in the complex plane. As a consequence he was able to show that if H2(μ) ≠ L2(μ), then every function f ∈ H2(μ) admits an analytic extension to a fixed open set Ω, thereby confirming in this context a phenomenon noted earlier in various situations by S. N. Bernštein, S. N. Mergelyan, and others. Here we present a new proof of Thomson’s results, based on Tolsa’s recent work on the semiadditivity of analytic capacity, which gives more information and is applicable to other problems as well.
Original language | English |
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Pages (from-to) | 217-238 |
Number of pages | 22 |
Journal | St. Petersburg Mathematical Journal |
Volume | 17 |
Issue number | 2 |
DOIs | |
State | Published - 2006 |
Keywords
- Analytic capacity
- Polynomial approximation
- Subnormal operators
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Applied Mathematics