Probability and a Dirichlet problem for multiply superharmonic functions

John B. Walsh

Annales de l'institut Fourier (1968)

  • Volume: 18, Issue: 2, page 221-279
  • ISSN: 0373-0956

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Walsh, John B.. "Probability and a Dirichlet problem for multiply superharmonic functions." Annales de l'institut Fourier 18.2 (1968): 221-279. <http://eudml.org/doc/73959>.

@article{Walsh1968,
author = {Walsh, John B.},
journal = {Annales de l'institut Fourier},
keywords = {partial differential equations},
language = {eng},
number = {2},
pages = {221-279},
publisher = {Association des Annales de l'Institut Fourier},
title = {Probability and a Dirichlet problem for multiply superharmonic functions},
url = {http://eudml.org/doc/73959},
volume = {18},
year = {1968},
}

TY - JOUR
AU - Walsh, John B.
TI - Probability and a Dirichlet problem for multiply superharmonic functions
JO - Annales de l'institut Fourier
PY - 1968
PB - Association des Annales de l'Institut Fourier
VL - 18
IS - 2
SP - 221
EP - 279
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/73959
ER -

References

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  1. [1] R. ARENS and I. M. SINGER, Function values as boundary integrals, Proc. Amer. Math. Soc. 5, (1954), 735-745. Zbl0056.33501MR16,373f
  2. [2] V. AVANISSIAN, Fonctions plurisousharmoniques et fonctions doublement sousharmoniques, Ann. Scient. Ec. Norm. Sup. 78 (1961), 101-161. Zbl0096.06103MR24 #A2052
  3. [3] H. BAUER, Šilovcher Rand und Dirichletsches Problem, Ann. Inst. Fourier 11 (1961), 89-136. Zbl0098.06902MR25 #443
  4. [4] S. BERGMAN, Functions of extended class in the theory of functions of several complex variables, Trans. Amer. Math. Soc. 63 (1948), 523-547. Zbl0034.05304MR10,30b
  5. [5] D. BLACKWELL, On a class of probability spaces, Proc. Third Berkeley Symp. on Stat. and Prob. (1956), 1-6. Zbl0073.12301MR18,940d
  6. [6] M. BRELOT, Éléments de la théorie classique du potentiel, Centre de Documentation Universitaire, Paris 1961. 
  7. [7] M. BRELOT, Le Problème de Dirichlet. Axiomatique et frontière de Martin ; J. de Math. 35 (1963), 297-334. Zbl0071.10001MR20 #6607
  8. [8] H. J. BREMERMANN, On the conjecture of equivalence of the plurisubharmonic functions and the Hartog functions, Math. Ann. 131 (1956), 76-86. Zbl0070.07603MR17,1070h
  9. [9] H. J. BREMERMANN, Note on plurisubharmonic functions and Hartogs functions, Proc. Amer. Math. Soc. 7 (1956), 771-775. Zbl0071.29403MR18,387f
  10. [10] H. J. BREMERMANN, On a generalized Dirichlet problem for plurisubharmonic functions and pseudo-convex domains, Trans. Amer. Math. Soc. 91 (1956), 246-276. Zbl0091.07501MR25 #227
  11. [11] K. L. CHUNG and J. L. DOOB, Fields, optionality and measurability, Amer. J. Math. 87 (1965), 397-424. Zbl0192.24604MR35 #4972
  12. [12] P. COURRÈGE and P. PRIOURET, Axiomatique du problème de Dirichlet et processus de Markov, Seminaire Brelot, Choquet et Deny 1963/1964. Zbl0132.33803
  13. [13] P. COURRÈGE and P. PRIOURET, Temps d'arrêt d'une fonction aléatoire : Relations d'équivalence associées et propriétés de décomposition, Publ. de l'Inst. de Statistique, Paris 14 (1965), 245-278. Zbl0287.60076MR36 #4640
  14. [14] P. COURRÈGE and P. PRIOURET, Recollements de processus de Markov, Ibid., 275-376. Zbl0281.60075MR36 #4641
  15. [15] J. L. DOOB, Semimartingales and subharmonic functions, Trans. Amer. Math. Soc. 77 (1954), 86-121. Zbl0059.12205MR16,269a
  16. [16] J. L. DOOB, A probability approach to the heat equation, Trans. Amer. Math. Soc. 80 (1955), 216-280. Zbl0068.32705MR18,76g
  17. [17] J. L. DOOB, Probability methods applied to the first boundary value problem, Proc. Third Berkeley Symp. on Stat. and Prob. (1956), 19-54. Zbl0074.09101MR18,941a
  18. [18] J. L. DOOB, Probability theory and the first boundary value problem, Ill. J. Math. 2 (1958), 19-36. Zbl0086.08403MR21 #5242
  19. [19] J. L. DOOB, Conditional Brownian motion and the boundary limits of harmonic functions, Bull. Soc. Math. France 85 (1957), 431-458. Zbl0097.34004MR22 #844
  20. [20] J. GORSKI, The method of extremal points and Dirichlet's problem in the space of two complex variables, Arch. Rat. Mech. Anal. 4 (1960), 412-427. Zbl0111.07902MR22 #4894
  21. [21] J. GORSKI, Remark on a certain theorem of H. J. Bremermann, Ann. Pol. Math. 11 (1962), 225-227. Zbl0111.08101MR25 #4125
  22. [22] P. R. HALMOS, Measure Theory, Van Nostrand, Princeton, 1950. Zbl0040.16802MR11,504d
  23. [23] G. A. HUNT, Markov processes and potentials, I, II, III. Ill. J. Math. 1 (1957), 44-93, 316-369 ; Ibid. 2 (1958), 151-213. Zbl0100.13804
  24. [24] N. IKEDA, M. NAGASAWA and S. WATANABE, A construction of Markov processes by piecing out, Proc. Japan Acad. 42 (1966) 370-375. Zbl0178.53401MR34 #2070
  25. [25] S. KAKUTANI, Two dimensional Brownian motion and harmonic functions, Proc. Imp. Acad. Tokyo 20 (1944), 706-714. Zbl0063.03107MR7,315b
  26. [26] I. KIMURA, Sur les fonctions plurisousharmoniques et les barriers, Proc. Japan Acad. 36 (1960), 639-643. Zbl0100.07901MR23 #A3278
  27. [27] H. KUNITA and T. WATANABE, (to appear). 
  28. [28] Y. KUSUNOKI, On a generalized Dirichlet problem for plurisubharmonic functions, J. Math. Kyoto Univ. 4 (1964), 123-147. Zbl0158.12704MR30 #4981
  29. [29] F. LEJA, Une méthode élémentaire de résolution de problème de Dirichlet dans le plan, Ann. Soc. Polon. Math. 23 (1950), 230-245. Zbl0039.32501MR12,703h
  30. [30] P. LELONG, Les fonctions plurisousharmoniques, Ann. Soc. Ec. Norm. Sup. 62 (1945), 301-338. Zbl0061.23205MR8,271f
  31. [31] M. LOÈVE, Probability Theory, Van Nostrand, Princeton, 1963. Zbl0108.14202MR34 #3596
  32. [32] R. S. MARTIN, Minimal positive harmonic functions, Trans. Amer. Math. Soc. 49 (1941), 137-172. Zbl0025.33302MR2,292hJFM67.0343.03
  33. [33] P. A. MEYER, Probability and Potentials, Blaisdell, 1966. Zbl0138.10401MR34 #5119
  34. [34] J. SICIAK, On function families with boundary, Pac. J. Math. 12 (1962), 375-384. Zbl0106.08801MR26 #1746
  35. [35] J. SICIAK, On some extremal functions and their applications to the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc. 105 (1962), 322-357. Zbl0111.08102MR26 #1495

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