On some translation invariant balayage spaces

Walter Hoh; Niels Jacob

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 3, page 471-478
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Hoh, Walter, and Jacob, Niels. "On some translation invariant balayage spaces." Commentationes Mathematicae Universitatis Carolinae 32.3 (1991): 471-478. <http://eudml.org/doc/247307>.

@article{Hoh1991,
abstract = {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.},
author = {Hoh, Walter, Jacob, Niels},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {balayage spaces; strong Feller semigroups; non-local potential theory; strong Feller semigroup; non-local potential theory},
language = {eng},
number = {3},
pages = {471-478},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On some translation invariant balayage spaces},
url = {http://eudml.org/doc/247307},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Hoh, Walter
AU - Jacob, Niels
TI - On some translation invariant balayage spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 3
SP - 471
EP - 478
AB - 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.
LA - eng
KW - balayage spaces; strong Feller semigroups; non-local potential theory; strong Feller semigroup; non-local potential theory
UR - http://eudml.org/doc/247307
ER -

References

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  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. Zbl0308.31001MR0481057
  2. Bliedtner J., Hansen W., Potential theory - An analytic and probabilistic approach to balayage, Universitext, Springer Verlag, Berlin-Heidelberg-New York-Tokyo, 1986. Zbl0706.31001MR0850715
  3. Brzezina M., On a class of translation invariant balayage spaces, to appear. Zbl0779.31005MR1214673
  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. (1972) Zbl0242.31011MR0322188
  6. Hawkes J., Potential theory of Lévy processes, Proc. London Math. Soc. (3) 38 (1979), 335-352. (1979) Zbl0401.60069MR0531166
  7. Jacob N., Sur les fonctions 2 r -harmoniques de N.S.Landkof, C.R. Acad. Sci. Paris 304 (1987), 169-171. (1987) Zbl0625.31003MR0880572
  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. MR0350027
  9. Riesz M., Intégrales de Riemann-Liouville et potentiels, Acta Szeged Sect. Math. 9 (1938), 1-42. (1938) Zbl0018.40704
  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. Zbl0232.42007MR0304972

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