A test of Picard principle for rotation free densities, II
Michihiko KAWAMURA, Mitsuru NAKAI
著者情報
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Michihiko KAWAMURA
Mathematical Institute Faculty of Education Fukui University
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Mitsuru NAKAI
Department of Mathematics Nagoya Institute of Technology
ジャーナル
フリー
1976 年 28 巻 2 号 p. 323-342
詳細
- Published: 1976 Received: 1975/04/24 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
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訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報 訂正内容: Wrong : 1) M. Brelot, Étude des l'équation de la chaleur Δu=c(M)u(M), c(M)_??_0, au voisinage d'un point singulier du coefficient, Ann. Sci. École Norm. Sup., 48 (1931), 153-246.
2) C. Constantinescu and A. Cornea, Über einige Problem von M. Heins, Rev. Roumaine Math. Pures Appl., 4 (1959), 277-281.
3) C. Constantinescu and A. Cornea, Ideale Ränder Riemannscher Flächen, Springer, 1963.
4) K. Hayashi, Les solutions positives de l'équation Δu=Pu sur une surface de Riemann, Kodai Math. Sem. Rep., 13 (1961), 20-24.
5) M. Hems, Riemann surfaces of infinite genus, Ann. of Math., 55 (1952), 296-317.
6) S. Ito, On existence of Green function and positive superharmonic functions for linear elliptic operators of second order, J. Math. Soc. Japan, 16 (1964), 299-306.
7) S. Ito, Martin boundary for linear elliptic differential operator of second order in a manifold, J. Math. Soc. Japan, 16 (1964), 307-334.
8) O. Kellog, Foundations of Potential Theory, Frederick Ungar, 1929.
9) Z. Kuramochi, An example of a null-boundary Riemann surface, Osaka Math. J., 6 (1954), 83-91.
10) A. Lahtinen, On the solutions of Δu=Pu for acceptable densities on open Riemann surfaces, Ann. Acad. Sci. Fenn., 515 (1972).
11) A. Lahtinen, On the equation Δu=Pu and the classification of acceptable densities on Riemann surfaces, Ann. Acad. Sci. Fenn., 533 (1973).
12) A. Lahtinen, On the existence of singular solutions of Δu=Pu on Riemann surfaces, Ann. Acad. Sci. Fenn., 546 (1973).
13) R. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc., 49 (1941), 137-172.
14) J. Milnor, Morse Theory, Ann. Math. Studies, 51 (1963).
15) C. Miranda, Partial differential Equations of Elliptic Type, Springer, 1970.
16) L. Myrberg, Über die Integration der Differentialgleichung Δu=c(P)u auf offenen Riemannschen Flächen, Math. Scand., 2 (1954), 142-152.
17) L. Myrberg, Über die Existenz der Greenschen Funktion der Gleichung Δu=c(P)u auf Riemannschen Flächen, Ann. Acad. Sci. Fenn., 170 (1954).
18) M. Nakai, The space of nonnegative solutions of the equation Δu=Pu on a Riemann surface, Kodai Math. Sem. Rep., 12 (1960), 151-178.
19) M. Nakai, Order comparisons on canonical isomorphisms, Nagoya Math. J., 50 (1973), 67-87.
20) M. Nakai, Martin boundary over an isolated singularity of rotation free density, J. Math. Soc. Japan, 26 (1974), 483-507.
21) M. Nakai, A test for Picard principle, Nagoya Math. J., 56 (1974), 105-119.
22) M. Nakai, A test of Picard principle for rotation free densities, J. Math. Soc. Japan, 27 (1975), 412-431.
23) M. Ozawa, Classification of Riemann surfaces, Kodai Math. Sem. Rep., 4 (1952), 63-76.
24) M. Ozawa, Some classes of positive solutions of Δu=Pu on Riemann surfaces, I, Kodai Math. Sem. Rep., 6 (1954), 121-126.
25) M. Ozawa, Some classes of positive solutions of Δu=Pu on Riemann surfaces, II, Kodai Math. Sem. Rep., 7 (1955), 15-20.
26) H. Royden, The equation Δu=Pu, and the classification of open Riemann surfaces, Ann. Acad. Sci. Fenn., 271 (1959).
27) I. Singer, Image set of reduction operator for Dirichlet finite solutions of Δu =Pu, Proc. Amer. Math. Soc., 32 (1972), 464-468.
28) I. Singer, Boundary isomorphism between Dirichlet finite solutions ofΔu=Pu and harmonic functions, Nagoya Math. J., 50 (1973), 7-20.
29) M. Šur, The Martin boundary for a linear elliptic second order operator, Izv. Akad. Nauk SSSR, 27 (1963), 45-60 (Russian).
30) M. Tsuji, Potential Theory in Moden Function Theory, Maruzen, 1959.
31) K. Yosida, Functional Analysis, Springer, 1965.
Right : [1] M. Brelot, Étude des l'équation de la chaleur Δu=c(M)u(M), c(M)≥0, au voisinage d'un point singulier du coefficient, Ann. Sci. École Norm. Sup., 48 (1931), 153-246.
[2] C. Constantinescu and A. Cornea, Über einige Problem von M. Heins, Rev. Roumaine Math. Pures Appl., 4 (1959), 277-281.
[3] C. Constantinescu and A. Cornea, Ideale Ränder Riemannscher Flächen, Springer, 1963.
[4] K. Hayashi, Les solutions positives de l'équation Δu=Pu sur une surface de Riemann, Kodai Math. Sem. Rep., 13 (1961), 20-24.
[5] M. Heins, Riemann surfaces of infinite genus, Ann. of Math., 55 (1952), 296-317.
[6] S. Itô, On existence of Green function and positive superharmonic functions for linear elliptic operators of second order, J. Math. Soc. Japan, 16 (1964), 299-306.
[7] S. Itô, Martin boundary for linear elliptic differential operator of second order in a manifold, J. Math. Soc. Japan, 16 (1964), 307-334.
[8] O. Kellog, Foundations of Potential Theory, Frederick Ungar, 1929.
[9] Z. Kuramochi, An example of a null-boundary Riemann surface, Osaka Math. J., 6 (1954), 83-91.
[10] A. Lahtinen, On the solutions of Δu=Pu for acceptable densities on open Riemann surfaces, Ann. Acad. Sci. Fenn., 515 (1972).
[11] A. Lahtinen, On the equation Δu=Pu and the classification of acceptable densities on Riemann surfaces, Ann. Acad. Sci. Fenn., 533 (1973).
[12] A. Lahtinen, On the existence of singular solutions of Δu=Pu on Riemann surfaces, Ann. Acad. Sci. Fenn., 546 (1973).
[13] R. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc., 49 (1941), 137-172.
[14] J. Milnor, Morse Theory, Ann. Math. Studies, 51 (1963).
[15] C. Miranda, Partial differential Equations of Elliptic Type, Springer, 1970.
[16] L. Myrberg, Über die Integration der Differentialgleichung Δu=c(P)u auf offenen Riemannschen Flächen, Math. Scand., 2 (1954), 142-152.
[17] L. Myrberg, Über die Existenz der Greenschen Funktion der Gleichung Δu=c(P)u auf Riemannschen Flächen, Ann. Acad. Sci. Fenn., 170 (1954).
[18] M. Nakai, The space of nonnegative solutions of the equation Δu=Pu on a Riemann surface, Kodai Math. Sem. Rep., 12 (1960), 151-178.
[19] M. Nakai, Order comparisons on canonical isomorphisms, Nagoya Math. J., 50 (1973), 67-87.
[20] M. Nakai, Martin boundary over an isolated singularity of rotation free density, J. Math. Soc. Japan, 26 (1974), 483-507.
[21] M. Nakai, A test for Picard principle, Nagoya Math. J., 56 (1974), 105-119.
[22] M. Nakai, A test of Picard principle for rotation free densities, J. Math. Soc. Japan, 27 (1975), 412-431.
[23] M. Ozawa, Classification of Riemann surfaces, Kodai Math. Sem. Rep., 4 (1952), 63-76.
[24] M. Ozawa, Some classes of positive solutions of Δu=Pu on Riemann surfaces, I, Kodai Math. Sem. Rep., 6 (1954), 121-126.
[25] M. Ozawa, Some classes of positive solutions of Δu=Pu on Riemann surfaces, II, Kodai Math. Sem. Rep., 7 (1955), 15-20.
[26] H. Royden, The equation Δu=Pu, and the classification of open Riemann surfaces, Ann. Acad. Sci. Fenn., 271 (1959).
[27] I. Singer, Image set of reduction operator for Dirichlet finite solutions of Δu=Pu, Proc. Amer. Math. Soc., 32 (1972), 464-468.
[28] I. Singer, Boundary isomorphism between Dirichlet finite solutions of Δu=Pu and harmonic functions, Nagoya Math. J., 50 (1973), 7-20.
[29] M. Šur, The Martin boundary for a linear elliptic second order operator, Izv. Akad. Nauk SSSR, 27 (1963), 45-60 (Russian).
[30] M. Tsuji, Potential Theory in Moden Function Theory, Maruzen, 1959.
[31] K. Yosida, Functional Analysis, Springer, 1965.
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