Hunt's hypothesis (H) and triangle property of the Green function

Hansen W, Netuka I (2016)
Expositiones Mathematicae 34(1): 95-100.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor*in
Hansen, WolfhardUniBi; Netuka, Ivan
Abstract / Bemerkung
Let X be a locally compact abelian group with countable base and let W be a convex cone of positive numerical functions on X which is invariant under the group action and such that (X, W) is a balayage space or (equivalently, if 1 epsilon W) such that W is the set of excessive functions of a Hunt process on X, W separates points, every function in W is the supremum of its continuous minorants in W, and there exist strictly positive continuous u, v epsilon W such that u/v -> 0 at infinity. Assuming that there is a Green function G > 0 for X which locally satisfies the triangle inequality G (x, z) A G (y, z) <= CG (x, y) (true for many Levy processes), it is shown that Hunt's hypothesis (H) holds, that is, every semipolar set is polar.
Stichworte
Hunt process; Levy process; Balayage space; Green function; 3G-property; Continuity principle; Polar set; Semipolar set; Hypothesis (H)
Erscheinungsjahr
2016
Zeitschriftentitel
Expositiones Mathematicae
Band
34
Ausgabe
1
Seite(n)
95-100
ISSN
0723-0869
eISSN
1878-0792
Page URI
https://pub.uni-bielefeld.de/record/2917172

Zitieren

Hansen W, Netuka I. Hunt's hypothesis (H) and triangle property of the Green function. Expositiones Mathematicae. 2016;34(1):95-100.
Hansen, W., & Netuka, I. (2016). Hunt's hypothesis (H) and triangle property of the Green function. Expositiones Mathematicae, 34(1), 95-100. doi:10.1016/j.exmath.2014.12.009
Hansen, W., and Netuka, I. (2016). Hunt's hypothesis (H) and triangle property of the Green function. Expositiones Mathematicae 34, 95-100.
Hansen, W., & Netuka, I., 2016. Hunt's hypothesis (H) and triangle property of the Green function. Expositiones Mathematicae, 34(1), p 95-100.
W. Hansen and I. Netuka, “Hunt's hypothesis (H) and triangle property of the Green function”, Expositiones Mathematicae, vol. 34, 2016, pp. 95-100.
Hansen, W., Netuka, I.: Hunt's hypothesis (H) and triangle property of the Green function. Expositiones Mathematicae. 34, 95-100 (2016).
Hansen, Wolfhard, and Netuka, Ivan. “Hunt's hypothesis (H) and triangle property of the Green function”. Expositiones Mathematicae 34.1 (2016): 95-100.