Jensen Measures in Potential Theory

Hansen W, Netuka I (2012)
Potential Analysis 37(1): 79-90.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor*in
Hansen, WolfhardUniBi; Netuka, Ivan
Abstract / Bemerkung
It is shown that, for open sets in classical potential theory and-more generally-for elliptic harmonic spaces Y, the set J (x) (Y) of Jensen measures (representing measures with respect to superharmonic functions on Y) for a point x aaEuro parts per thousand Y is a simple union of closed faces of the compact convex set of representing measures with respect to potentials on Y, a set which has been thoroughly studied a long time ago. In particular, the set of extreme Jensen measures can be immediately identified. The results hold even without ellipticity (thus capturing also many examples for the heat equation) provided a rather weak approximation property for superharmonic functions holds. Equally sufficient are a certain transience property and a weak regularity property. More important, each of these properties turns out to be necessary and sufficient for obtaining (in the classical case) that J (x) (Y) coincides with the set of all compactly supported probability measures in .
Stichworte
Representing measure; Jensen measure; Harmonic measure; Superharmonic; function; Potential; Harmonic space; Balayage; Fine topology; Face of a; Extreme point; convex set
Erscheinungsjahr
2012
Zeitschriftentitel
Potential Analysis
Band
37
Ausgabe
1
Seite(n)
79-90
ISSN
0926-2601
Page URI
https://pub.uni-bielefeld.de/record/2517901

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Hansen W, Netuka I. Jensen Measures in Potential Theory. Potential Analysis. 2012;37(1):79-90.
Hansen, W., & Netuka, I. (2012). Jensen Measures in Potential Theory. Potential Analysis, 37(1), 79-90. doi:10.1007/s11118-011-9247-8
Hansen, W., and Netuka, I. (2012). Jensen Measures in Potential Theory. Potential Analysis 37, 79-90.
Hansen, W., & Netuka, I., 2012. Jensen Measures in Potential Theory. Potential Analysis, 37(1), p 79-90.
W. Hansen and I. Netuka, “Jensen Measures in Potential Theory”, Potential Analysis, vol. 37, 2012, pp. 79-90.
Hansen, W., Netuka, I.: Jensen Measures in Potential Theory. Potential Analysis. 37, 79-90 (2012).
Hansen, Wolfhard, and Netuka, Ivan. “Jensen Measures in Potential Theory”. Potential Analysis 37.1 (2012): 79-90.