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Weak compactness of
representing measures for R(K)
Theodore William Gamelin |
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Vol. 114 (1984), No. 1, 95–107
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Abstract |
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Let K be a compact subset of the complex plane, with connected interior K∘. Suppose that p ∈ K∘ has a weakly compact set of representing measures on ∂K with respect to the algebra R(K), Then every representing measure for p is mutually absolutely continuous with respect to harmonic measure, as is every nonzero orthogonal measure on ∂K. A class of champagne bubble sets with weakly compact sets of representing measures is constructed. |
Mathematical Subject Classification 2000
Primary: 46J10
Secondary: 30H05, 46E27, 46J15
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Milestones
Received: 15 September 1982
Revised: 20 February 1983
Published: 1 September 1984
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Authors |
| Theodore William Gamelin | |
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