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Analytic Structures for H∞ of Certain Domains in Cn

Published online by Cambridge University Press:  20 November 2018

Eric P. Kronstadt
Eric P. Kronstadt*
Affiliation:
University of Michigan, Ann Arbor, Michigan
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Let Ω C Cn be a bounded domain; let H∞ (Ω) be the uniform algebra of bounded analytic functions on 12; and let ∑ (Ω) be the maximal ideal space of H∞ (Ω). In the weak-* topology of (H∞ (Ω))*, ∑ (Ω) is a compact Hausdorf space in which Ω is embedded in a natural fashion, so that to every g ∈ H∞ (Ω) there corresponds the Gelfand transform ĝ ∈ C(∑ (Ω)); ĝ|Ω = g.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 4 , 01 August 1978 , pp. 863 - 871
Copyright
Copyright © Canadian Mathematical Society 1978

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