منابع مشابه
Reduced functions and Jensen measures
Let φ be a locally upper bounded Borel measurable function on a Greenian open set Ω in Rd and, for every x ∈ Ω, let vφ(x) denote the infimum of the integrals of φ with respect to Jensen measures for x on Ω. Twenty years ago, B.J. Cole and T.J. Ransford proved that vφ is the supremum of all subharmonic minorants of φ on X and that the sets {vφ < t}, t ∈ R, are analytic. In this paper, a differen...
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In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point. In [Co] Cole gave a counterexample to the peak point conjecture by constructing a non-trivial uniform algebra A with co...
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Let (X,H) be a P-harmonic space and assume for simplicity that constants are harmonic. Given a numerical function φ on X which is locally lower bounded, let Jφ(x) := sup{ ∫ ∗ φdμ(x) : μ ∈ Jx(X)}, x ∈ X, where Jx(X) denotes the set of all Jensen measures μ for x, that is, μ is a compactly supported measure on X satisfying ∫ u dμ ≤ u(x) for every hyperharmonic function on X. The main purpose of t...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1980
ISSN: 0022-1236
DOI: 10.1016/0022-1236(80)90078-6