Martin boundary over an isolated singularity of rotation free density

Mitsuru NAKAI

doi:10.2969/jmsj/02630483

Mitsuru NAKAI

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JOURNAL FREE ACCESS

1974 Volume 26 Issue 3 Pages 483-507

DOI https://doi.org/10.2969/jmsj/02630483

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Published: 1974 Received: June 25, 1973 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. Brelot, Étude des intégrales de la chaleur Δu=cu, c_??_0, au voisinage d'un point singulier du coefficient, Ann. Sci., Ecole Norm. Sup., 48 (1931), 153-246.
2) C. Constantinescu und A. Cornea, Über einige Problem von M. Heins, Rev. Roumaine Math. Pures Appl., 4 (1959), 277-281.
3) C. Constantinescu und A. Cornea, Ideale Ränder Riemannscher Flächen, Springer, 1963.
4) M. Heins, Riemann surfaces of infinite genus, Ann. of Math., 55 (1952), 296-317.
5) S. Ito, On existence of Green functions and positive superharmonic functions for linear elliptic operators of second order, J. Math. Soc. Japan, 16 (1964), 299-306.
6) S. Ito, Martin boundary for linear elliptic differential operators of second order in a manifold, J. Math. Soc. Japan, 16 (1964), 307-334.
7) O. Kellog, Foundations of Potential Theory, Frederick Ungar, 1929.
8) Z. Kuramochi, An example of a null-boundary Riemann surface, Osaka Math. J., 6 (1954), 83-91.
9) R. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc., 49 (1941), 137-172.
10) C. Miranda, Partial Differential Equations of Elliptic Type, Springer, 1970.
11) L. Myrberg, Über die Integration der Differential Gleichung Δu=c(P)u auf offenen Riemannschen Flächen, Math. Scand., 2 (1954), 142-152.
12) L. Myrberg, Über die Existenz der Greenschen Funktion der Gleichung Δu= c(P)u auf Riemannschen Flächen, Ann. Acad. Sci. Fenn., 170 (1954).
13) M. Nakai, The space of non-negative solutions of the equation Δu=Pu on a Riemann surface, Kôdai Math. Sem. Rep., 12 (1960), 151-178.
14) M. Nakai, Order comparisons on canonical isomorphisms, Nagoya Math. J., 50 (1973), 67-88.
15) M. Ozawa, Some classes of positive solutions of Δu=Pu on Riemann urfaces, I, Kôdai Math. Sem. Rep., 6 (1954), 121-126.
16) M. Ozawa, Some classes of positive solutions of Δu=Pu on Riemann surfaces, II, Kôdai Math. Sem. Rep., 7 (1955), 15-20.
17) H. Royden, The equation Δu=Pu, and the classification of open Riemann surfaces, Ann. Acad. Sci. Fenn., 271 (1959), 1-27.
18) M. Šur, The Martin boundary for a linear elliptic second order operator, Izv. Akad. Nauk SSSR, 27 (1963), 45-60 (Russian).
19) M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, 1959.

Right : [1] M. Brelot, Étude des intégrales de la chaleur Δu=cu, c≥0, au voisinage d'un point singulier du coefficient, Ann. Sci., Ecole Norm. Sup., 48 (1931), 153-246.
[2] C. Constantinescu und A. Cornea, Über einige Problem von M. Heins, Rev. Roumaine Math. Pures Appl., 4 (1959), 277-281.
[3] C. Constantinescu und A. Cornea, Ideale Ränder Riemannscher Flächen, Springer, 1963.
[4] M. Heins, Riemann surfaces of infinite genus, Ann. of Math., 55 (1952), 296-317.
[5] S. Itô, On existence of Green functions and positive superharmonic functions for linear elliptic operators of second order, J. Math. Soc. Japan, 16 (1964), 299-306.
[6] S. Itô, Martin boundary for linear elliptic differential operators of second order in a manifold, J. Math. Soc. Japan, 16 (1964), 307-334.
[7] O. Kellog, Foundations of Potential Theory, Frederick Ungar, 1929.
[8] Z. Kuramochi, An example of a null-boundary Riemann surface, Osaka Math. J., 6 (1954), 83-91.
[9] R. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc., 49 (1941), 137-172.
[10] C. Miranda, Partial Differential Equations of Elliptic Type, Springer, 1970.
[11] L. Myrberg, Über die Integration der Differential Gleichung Δu=c(P)u auf offenen Riemannschen Flächen, Math. Scand., 2 (1954), 142-152.
[12] L. Myrberg, Über die Existenz der Greenschen Funktion der Gleichung Δu= c(P)u auf Riemannschen Flächen, Ann. Acad. Sci. Fenn., 170 (1954).
[13] M. Nakai, The space of non-negative solutions of the equation Δu=Pu on a Riemann surface, Kôdai Math. Sem. Rep., 12 (1960), 151-178.
[14] M. Nakai, Order comparisons on canonical isomorphisms, Nagoya Math. J., 50 (1973), 67-88.
[15] M. Ozawa, Some classes of positive solutions of Δu=Pu on Riemann surfaces, I, Kôdai Math. Sem. Rep., 6 (1954), 121-126.
[16] M. Ozawa, Some classes of positive solutions of Δu=Pu on Riemann surfaces, II, Kôdai Math. Sem. Rep., 7 (1955), 15-20.
[17] H. Royden, The equation Δu=Pu, and the classification of open Riemann surfaces, Ann. Acad. Sci. Fenn., 271 (1959), 1-27.
[18] M. Šur, The Martin boundary for a linear elliptic second order operator, Izv. Akad. Nauk SSSR, 27 (1963), 45-60 (Russian).
[19] M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, 1959.

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