It is well known that strong Feller semigroups generate balayage spaces provided the set of their excessive functions contains sufficiently many elements. In this note, we give explicit examples of strong Feller semigroups which do generate balayage spaces. Further we want to point out the role of the generator of the semigroup in the related potential theory.
@article{118428, author = {Walter Hoh and Niels Jacob}, title = {On some translation invariant balayage spaces}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {32}, year = {1991}, pages = {471-478}, zbl = {0755.31012}, mrnumber = {1159795}, language = {en}, url = {http://dml.mathdoc.fr/item/118428} }
Hoh, Walter; Jacob, Niels. On some translation invariant balayage spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 471-478. http://gdmltest.u-ga.fr/item/118428/
Potential theory on locally compact Abelian groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, II. Ser. Bd. 87, Springer Verlag, Berlin-Heidelberg-New York, 1975. | MR 0481057 | Zbl 0308.31001
Potential theory - An analytic and probabilistic approach to balayage, Universitext, Springer Verlag, Berlin-Heidelberg-New York-Tokyo, 1986. | MR 0850715 | Zbl 0706.31001
On a class of translation invariant balayage spaces, to appear. | MR 1214673 | Zbl 0779.31005
Méthodes Hilbertiennes et théorie du potentiel, In Potential Theory, C.I.M.E., Roma (1970), 123-201.
Symmetric harmonic groups and translation invariant Dirichlet spaces, Invent. Math. 18 (1972), 143-182. (1972) | MR 0322188 | Zbl 0242.31011
Potential theory of Lévy processes, Proc. London Math. Soc. (3) 38 (1979), 335-352. (1979) | MR 0531166 | Zbl 0401.60069
Sur les fonctions $2r$-harmoniques de N.S.Landkof, C.R. Acad. Sci. Paris 304 (1987), 169-171. (1987) | MR 0880572 | Zbl 0625.31003
Foundation of modern potential theory, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 180, Springer Verlag, Berlin - Heidelberg - New York, 1972. | MR 0350027
Intégrales de Riemann-Liouville et potentiels, Acta Szeged Sect. Math. 9 (1938), 1-42. (1938) | Zbl 0018.40704
Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, Vol. 32, Princeton University Press, Princeton, New Jersey, 1971. | MR 0304972 | Zbl 0232.42007