H -cones and potential theory

Nicu Boboc; Gheorghe Bucur; A. Cornea

Annales de l'institut Fourier (1975)

  • Volume: 25, Issue: 3-4, page 71-108
  • ISSN: 0373-0956

Abstract

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The H -cone is an abstract model for the cone of positive superharmonic functions on a harmonic space or for the cone of excessive functions with respect to a resolvent family, having sufficiently many properties in order to develop a good deal of balayage theory and also to construct a dual concept which is also an H -cone. There are given an integral representation theorem and a representation theorem as an H -cone of functions for which fine topology, thinnes, negligible sets and the sheaf property are studied with respect to the fine topology.

How to cite

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Boboc, Nicu, Bucur, Gheorghe, and Cornea, A.. "$H$-cones and potential theory." Annales de l'institut Fourier 25.3-4 (1975): 71-108. <http://eudml.org/doc/74261>.

@article{Boboc1975,
abstract = {The $H$-cone is an abstract model for the cone of positive superharmonic functions on a harmonic space or for the cone of excessive functions with respect to a resolvent family, having sufficiently many properties in order to develop a good deal of balayage theory and also to construct a dual concept which is also an $H$-cone. There are given an integral representation theorem and a representation theorem as an $H$-cone of functions for which fine topology, thinnes, negligible sets and the sheaf property are studied with respect to the fine topology.},
author = {Boboc, Nicu, Bucur, Gheorghe, Cornea, A.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3-4},
pages = {71-108},
publisher = {Association des Annales de l'Institut Fourier},
title = {$H$-cones and potential theory},
url = {http://eudml.org/doc/74261},
volume = {25},
year = {1975},
}

TY - JOUR
AU - Boboc, Nicu
AU - Bucur, Gheorghe
AU - Cornea, A.
TI - $H$-cones and potential theory
JO - Annales de l'institut Fourier
PY - 1975
PB - Association des Annales de l'Institut Fourier
VL - 25
IS - 3-4
SP - 71
EP - 108
AB - The $H$-cone is an abstract model for the cone of positive superharmonic functions on a harmonic space or for the cone of excessive functions with respect to a resolvent family, having sufficiently many properties in order to develop a good deal of balayage theory and also to construct a dual concept which is also an $H$-cone. There are given an integral representation theorem and a representation theorem as an $H$-cone of functions for which fine topology, thinnes, negligible sets and the sheaf property are studied with respect to the fine topology.
LA - eng
UR - http://eudml.org/doc/74261
ER -

References

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  1. [1] N. BOBOC, Sur les noyaux sur un espace mesurable, Principe de domination, Rev. Roumaine Math. Pures et Appl., n° 6 (1969). Zbl0182.15001MR43 #468
  2. [2] N. BOBOC, Gh. BUCUR and A. CORNEA, Cones of potentials on topological spaces, Rev. Roumaine Math. Pures et Appl., n° 6 (1973). Zbl0271.54009
  3. [3] N. BOBOC, C. CONSTANTINESCU and A. CORNEA, Semigroups of transitions on harmonic spaces, Rev. Roumaine Math. Pures et Appl., n° 6 (1967). Zbl0155.17302MR37 #1641
  4. [4] N. BOBOC et A. CORNEA, Cônes convexes ordonnés. H-cônes et adjoints de H-cônes, C. R. Acad. Sci. Paris, Sér. A, 270 (1970), 598-599. Zbl0188.17401
  5. [5] N. BOBOC et A. CORNEA, Cônes convexes ordonnés. H-cônes et biadjoints des H-cônes, C. R. Acad. Sci. Paris, Sér. A, 270 (1970), 1679-1682. Zbl0195.39903MR42 #7929
  6. [6] N. BOBOC et A. CORNEA, Cônes convexes ordonnés. Représentations intégrales, C. R. Acad. Sci. Paris, Sér. A, 271 (1970), 880-883. Zbl0211.13901MR49 #7469
  7. [7] M. BRELOT, Lectures on potential theory, Tata Institut Bombay, 1970. 
  8. [8] C. CONSTANTINESCU and A. CORNEA, Potential theory on Harmonic Spaces, Berlin-Heidelberg-New York, Springer, 1972. Zbl0248.31011MR54 #7817
  9. [9] B. FUGLEDE, Finely harmonic functions, Lecture Notes in Mathematics 289, 1972, Berlin-Heidelberg, New York, Springer. Zbl0248.31010MR56 #8883
  10. [10] R. M. HERVÉ, Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier, 12 (1962), 415-571. Zbl0101.08103MR25 #3186
  11. [11] P. A. MEYER, Représentation intégrale des fonctions excessives, pp. 196-208, Séminaire de probabilité V. Université de Strasbourg, Lecture Notes in Math., 1971. Zbl0256.60050MR51 #13260
  12. [12] G. MOKOBODZKI, Structure des cônes de potentiels, Séminaire Bourbaki, n° 377, 1969-1970. Zbl0208.36903
  13. [13] G. MOKOBODZKI, Densité relative des deux potentiels comparables, Séminaire de Probabilité IV. Université de Strasbourg, 1970 Lecture Notes in Mathematics. Zbl0218.31014MR45 #3747

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