The Measure Spectrum of a Uniform Algebra and Subharmonicity
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Let A be a uniform algebra on a compact Hausdorff space X. The spectrum, or the maximal ideal space, MA, of A is given byWe define the measure spectrum, SA, of A bySA is the set of all representing measures on X for all Φ ∈ MA. (A representing measure for Φ ∈ MA is a probability measure μ on X satisfyingThe concept of representing measure continues to be an effective tool in the study of uniform algebras. See for example [12, Chapters 2 and 3], [5, pp. 15-22] and [3]. Most of the known results on the subject of representing measures, however, concern measures associated with a single homomorphism.
1990 ◽
Vol 42
(5)
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pp. 776-789
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2010 ◽
Vol 88
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pp. 289-300
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1974 ◽
Vol 26
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pp. 405-411
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2005 ◽
Vol 48
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pp. 219-229
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2002 ◽
Vol 72
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pp. 1-12
1994 ◽
Vol 05
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pp. 201-212
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1971 ◽
Vol 23
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pp. 468-480
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1979 ◽
Vol 31
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pp. 79-86
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