[go: up one dir, main page]

 

  Previous |  Up |  Next

Article

Keywords:
balayage spaces; strong Feller semigroups; non-local potential theory
Summary:
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.
References:
[1] Berg C., Forst G.: 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
[2] Bliedtner J., Hansen W.: Potential theory - An analytic and probabilistic approach to balayage. Universitext, Springer Verlag, Berlin-Heidelberg-New York-Tokyo, 1986. MR 0850715 | Zbl 0706.31001
[3] Brzezina M.: On a class of translation invariant balayage spaces. to appear. MR 1214673 | Zbl 0779.31005
[4] Deny J.: Méthodes Hilbertiennes et théorie du potentiel. In Potential Theory, C.I.M.E., Roma (1970), 123-201.
[5] Forst G.: Symmetric harmonic groups and translation invariant Dirichlet spaces. Invent. Math. 18 (1972), 143-182. MR 0322188 | Zbl 0242.31011
[6] Hawkes J.: Potential theory of Lévy processes. Proc. London Math. Soc. (3) 38 (1979), 335-352. MR 0531166 | Zbl 0401.60069
[7] Jacob N.: Sur les fonctions $2r$-harmoniques de N.S.Landkof. C.R. Acad. Sci. Paris 304 (1987), 169-171. MR 0880572 | Zbl 0625.31003
[8] Landkof N.S.: Foundation of modern potential theory. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 180, Springer Verlag, Berlin - Heidelberg - New York, 1972. MR 0350027
[9] Riesz M.: Intégrales de Riemann-Liouville et potentiels. Acta Szeged Sect. Math. 9 (1938), 1-42. Zbl 0018.40704
[10] Stein E.M., Weiss G.: Introduction to Fourier analysis on Euclidean spaces. Princeton Mathematical Series, Vol. 32, Princeton University Press, Princeton, New Jersey, 1971. MR 0304972 | Zbl 0232.42007
Partner of
EuDML logo