# $H$-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

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topBoboc, 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

top- [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] 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] 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] 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] 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] 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] M. BRELOT, Lectures on potential theory, Tata Institut Bombay, 1970.
- [8] C. CONSTANTINESCU and A. CORNEA, Potential theory on Harmonic Spaces, Berlin-Heidelberg-New York, Springer, 1972. Zbl0248.31011MR54 #7817
- [9] B. FUGLEDE, Finely harmonic functions, Lecture Notes in Mathematics 289, 1972, Berlin-Heidelberg, New York, Springer. Zbl0248.31010MR56 #8883
- [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] 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] G. MOKOBODZKI, Structure des cônes de potentiels, Séminaire Bourbaki, n° 377, 1969-1970. Zbl0208.36903
- [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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