Abstract
In the frame of standard H-cones of functions (the cone of all excessive functions with respect to a submarkovian resolvent of kernels with reference measure on a measurable space) on a Green set we show that the cofine closure of the complement of an absorbent set in coabsorbent. We obtain different characterizations concerning the parabolicity, ellipticity and quasiellipticity in terms of the Green function. We also show that these notions are the same in the direct and the dual theory.
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Ben Saad, H. and Janßen, K.: ‘A characterization of parabolic potential theory,’Math. Ann. 272 (1985), 281–289.
Beznea L.: ‘Parabolic and elliptic parts in standard H-cones of functions,’,Rev. Roumaine Math. Pures Appl. 32 (1987), 875–880.
Beznea L. and Boboc N.: ‘Balayages absorbants, paraboliques, elliptiques et quasi elliptiques dans la théorie du potentiel; relations avec la fonction de Green’,C.R. Acad. Sci. Paris 315 (1992), Série I, 685–688.
Beznea L. and Boboc N.: ‘Absorbent, parabolic, elliptic and quasielliptic balayages in potential theory’,Rev. Roumaine Math. Pures Appl. 38 (1993), 197–234.
Beznea L. and Boboc N.: ‘Absorbent, parabolic, elliptic and quasielliptic balayages in potential theory; II’ (to appear)
Blumenthal R. M. and Getoor R. K.:Markov Processes and Potential Theory, Academic Press, 1968.
Blumenthal R. M. and Getoor R. K.: ‘Dual processes and potential theory’,Proc. 12th Biennial Seminar, Canadian Math. Congr. (1970), 137–156.
Boboc N. and Bucur Gh.: ‘Potentials in standard H-cones of functions’,Rev. Roumaine Math. Pures Appl. 33 (1988), 821–836.
Boboc N., Bucur Gh. and Cornea A.:Order and Convexity in Potential Theory: H-cones, Lecture Notes in Math. 853, Springer-Verlag, 1981.
Constantinescu C. and Cornea A.:Potential Theory on Harmonic Spaces, Springer-Verlag, 1972.
Ikegami T.: ‘Duality on harmonic spaces,’Osaka J. Math. 28 (1991), 93–116.
Král J., Lukeš J. and Netuka I.: ‘Elliptic points in one-dimensional harmonic spaces,’Comment. Math. Univ. Carolinae 12 (1971), 453–483.
Schirmeier U.: ‘Konvergenzeigenschaften in harmonischen Räumen,’Inv. Math. 55 (1979), 71–95.
Schirmeier U.: ‘Continuity properties of the carrier map,’Rev. Roumaine Math. Pures Appl. 28 (1988), 431–451.
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Beznea, L., Boboc, N. Absorbent, parabolic, elliptic and quasielliptic balayages in potential theory; relationships with the Green function. Potential Anal 4, 101–117 (1995). https://doi.org/10.1007/BF01275585
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DOI: https://doi.org/10.1007/BF01275585