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Das Picard-Prinzip und verwandte Fragen bei Störungen von harmonischen Räumen. (German) Zbl 0377.31011


MSC:

31C99 Generalizations of potential theory
31D05 Axiomatic potential theory
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References:

[1] Bauer, H.: Harmonische Räume und ihre Potentialtheorie. Lecture Notes in Mathematics 22. Berlin-Heidelberg-New York: Springer 1966 · Zbl 0142.38402
[2] Brelot, M.: Étude de l’équation de la chaleur ?u=c(M)u(M), c(M) ?0, au voisinage d’un point singulier du coefficient. Ann. Sci. École Norm. Sup.48, 153-246 (1931) · Zbl 0002.25902
[3] Brelot, M.: On topologies and boundaries in potential theory. Lecture Notes in Mathematics 175. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0222.31014
[4] Brelot, M.: Sur l’allure à la frontière des familles de fonctions harmoniques ou surharmoniques. Rend. Math. (6) 8 No. 2, 447-456 (1975) · Zbl 0322.31014
[5] Constantinescu, C., Cornea, A.: Potential theory on harmonic spaces. Berlin-Heidelberg-New York: Springer 1972 · Zbl 0248.31011
[6] Hansen, W.: Potentialtheorie harmonischer Kerne. In: Seminar über Potentialtheorie, 103-159, Lecture Notes in Mathematics 69. Berlin-Heidelberg-New York: Springer 1968
[7] Hansen, W.: Cohomology in Harmonic Spaces. In: Seminar on potential theory II, 63-101. Lecture Notes in Mathematics 226. Berlin-Heidelberg-New York: Springer 1971
[8] Hansen, W.: Perturbation of Harmonic Spaces and Construction of Semigroups. Invent. math.19, 149-164 (1973) · Zbl 0258.31005 · doi:10.1007/BF01418925
[9] Helms, L. L.: Einführung in die Potentialtheorie. Berlin-New York: Wiley-Interscience 1969 · Zbl 0276.31001
[10] Hervé, R.M.: Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel. Ann. Inst. Fourier12, 415-571 (1962) · Zbl 0101.08103
[11] Hervé, R.M., Hervé, M.: Les fonctions surharmoniques associées à un operateur elliptique du second ordre à coefficients discontinus. Ann. Inst. Fourier19, 305-359 (1969) · Zbl 0176.09801
[12] Hueber, H.: Über die Existenz harmonischer Minoranten von super-harmonischen Funktionen. Math. Ann.225, 99-114 (1977) · Zbl 0332.31008 · doi:10.1007/BF01351714
[13] Maeda, F. Y.: Energy of functions on a self-adjoint harmonic space. I. Hiroshima Math. J. 313-337 (1972) · Zbl 0273.31015
[14] Nakai, M.: A test for Picard principle. Nagoya Math. J.56, 105-119 (1974) · Zbl 0304.31002
[15] Nakai, M.: Martin boundary over an isolated singularity of rotation free density. J. Math. Soc. Japan56, 483-507 (1974) · Zbl 0281.30012 · doi:10.2969/jmsj/02630483
[16] Kawamura, M., Nakai, M.: A test of Picard principle for rotation free densities II. J. Math. Soc. Japan28, 323-342 (1976) · Zbl 0341.30019 · doi:10.2969/jmsj/02820323
[17] Sieveking, M.: Integraldarstellung superharmonischer Funktionen mit Anwendung auf parabolische Differentialgleichungen. In: Seminar über Potentialtheorie, 13-68, Lecture Notes in Mathematics 69. Berlin-Heidelberg-New York: Springer 1968
[18] Sieveking, M.: Über die Greensche Funktion in der Potentialtheorie. (Nicht veröffentlicht)
[19] Walsh, B.: Perturbation of Harmonic Structures and an Index-zero Theorem. Ann. Inst. Fourier20, 317-359 (1970) · Zbl 0187.04303
[20] Walsh, B.: The theory of harmonic spaces. Canad. Math. Congress2, 183-187, Montreal, Que., 1975.
[21] Brelot, M.: Sur le principe des singularités positives et la notion de source pour l’équation ?u(M)=c(M)u(M) (c?0). Ann. Univ. Lyon section AXI, 9
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