Characterization of quasi-units in terms of equilibrium potentials

Authors:
Maynard Arsove and Heinz Leutwiler

Journal:
Proc. Amer. Math. Soc. **89** (1983), 267-272

MSC:
Primary 31D05

DOI:
https://doi.org/10.1090/S0002-9939-1983-0712635-7

MathSciNet review:
712635

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Abstract: In the cone of nonnegative superharmonic functions on a bounded euclidean region , quasi-units were introduced as those elements invariant under the infinitesimal generator of the fundamental one-parameter semigroup of operators . All harmonic measures and capacitary potentials are quasi-units, but the latter class has more extensive closure properties. Quasi-units arise naturally under various operations of classical potential theory and have important applications, for example in proving that the convex set of Green's potentials of positive mass distributions on with has as its extreme points precisely the capacitary potentials. Some new properties of quasi-units are developed here. In particular, it is shown that quasi-units can be characterized as limits of increasing sequences of continuous equilibrium potentials for which the equilibrium values tend to 1.

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0712635-7

Article copyright:
© Copyright 1983
American Mathematical Society