Hunt processes and analytic potential theory on rigged Hilbert spaces

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1. [1] S. Albeverio, R. Høegh-Krohn, Quasi invariant measures, symmetric diffusion processes and quantum fields, in Les méthodes mathématiques de la théorie quantique des champs, Colloques Internationaux du C. N. R. S., n° 248, Marseille, 23-27 juin 1975, C. N. R. S., 1976. 
2. [2] S. Albeverio, R. Høegh-Krohn, Dirichlet forms and diffusion processes on rigged Hilbert spaces, Zeitschr. f. Wahrscheinlich Keitsth. verw. Geb., 1977. Zbl0342.60057
3. [3] S. Albeverio, R. Høegh-Krohn, Canonical quantum fields in two space-time dimensions, Oslo University Preprint, March 1976 (to be published). 
4. [4] S. Albeverio, R. Høegh-Krohn, in the « Proceedings of the IV. International Symposium on Information Theory », Leningrad, June 1976, Akad. Nauk. SSSR, Moscow-Leningrad, 1976. Zbl0337.28009
5. [5] M. Fukushima, On boundary conditions for multidimensional Brownian motion with symmetric resolvents, J. Math. Soc. Japan, t. 21, 1969, p. 485-526. Zbl0181.20903MR236998
6. [6] M. Fukushima, Regular representations of Dirichlet spaces, Trans. Amer. Math. Soc., t. 155, 1971, p. 455-473. Zbl0248.31007MR281256
7. [7] M. Fukushima, Dirichlet spaces and strong Markov processes, Trans. Amer. Math. Soc., t. 162, 1971, p. 185-224. Zbl0254.60055MR295435
8. [8] M. Fukushima, On the generation of Markov processes by symmetric forms, in Proceedings of the Second Japan-USSR Symposium on Probability Theory, Springer, Berlin, 1973, p. 46-79. Zbl0262.60054MR494513
9. [9] M. Fukushima, Local property of Dirichlet forms and continuity of sample paths, Zeitschr. f. Wahrsch. u. verw. Geb., t. 29, 1974, p. 1-6. Zbl0283.60067MR365726
10. [10] M. Silverstein, Symmetric Markov processes, Springer, Berlin, 1974. Zbl0296.60038MR386032
11. [11] M. Silverstein, Boundary theory for symmetric Markov processes, Springer, Berlin, 1976. Zbl0331.60046MR451422
12. [12] H. Cartan, Théorie générale du balayage en potentiel newtonien, Ann. Univ. Grenoble, Sect. Sci. Math. Phys. (N. S.), t. 22, 1946, p. 221-280. Zbl0061.22701MR20682
13. [13] A. Beurling, J. Deny, Dirichlet spaces, Proc. Nat. Acad. Sci., USA, t. 45, 1959, p. 208-215. Zbl0089.08201MR106365
14. [14] J. Deny, Méthodes Hilbertiennes en théorie du potentiel, in Potential Theory, C. I. M. E., Cremonese, Roma, 1970, p. 121-201. Zbl0212.13401MR284609
15. [15] J. Deny, Théorie de la capacité dans les espaces fonctionnels, Séminaire Brelot-Choquet-Deny (Théorie du potentiel), 9e année, n° 1, 1964-1965. Zbl0138.36605MR190367
16. [16] M. Ito, A note on extended regular functional spaces, Proc. Jap. Acad. Sci., t. 43, 1967, p. 435-440. Zbl0156.33901MR227454
17. [17] H. Kunita, General boundary conditions for multidimensional diffusion processes, J. Math. Kyoto Univ., t. 10, 1970, p. 273-335. Zbl0204.41502MR270445
18. [18] J. Bliedtner, Dirichlet forms on regular function spaces, in « Seminar on Potential Theory II », p. 15-62, Lecture Notes in Math., 226, Springer, Berlin, 1971. MR399490
19. [19] M. Reed, B. Simon, in « Methods of Modern Mathematical Physics » III, to appear (Academ. Press, New York). Zbl0405.47007MR529429
20. [20] E.B. Dynkin, Markoi, processes, vol. I, II, Springer, Berlin, 1965 (transl.). 
21. [21] G.A. Hunt, Martingales et Processus de Markov, Dunod, Paris, 1966. Zbl0158.35802MR211453
22. [22] R.M. Blumenthal, R.K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. Zbl0169.49204MR264757
23. [23] P.A. Meyer, Probability and potentials, Ginn, Blaisdell, Waltham, 1966. C. Dellacherie, P.A. Meyer, Probabilités et potentiels, Herman, Paris, 1975. Zbl0138.10401MR205288
24. [24] P.A. Meyer, Processus de Markov, Springer, Berlin, 1967. Zbl0189.51403MR219136
25. [25] Y.L. Daletskii, Infinite dimensional elliptic operators and the corresponding parabolic equations, Russ. Math. Surv., t. 22, n° 4, 1967, p. 1-53 (transl.). Zbl0164.41304
26. [26] L. Gross, Potential theory on Hilbert space, J. Funct. Anal., t. 1, 1967, p. 123-181. Zbl0165.16403MR227747
27. [27] J. Kuelbs, Abstract Wiener spaces and applications to analysis, Pac. J. Math., t. 31, 1969, p. 433-450. Zbl0187.07001MR252597
28. [28] A. Piech, Diffusion semigroups on abstract Wiener space, Trans. Amer. Math. Soc., t. 166, 1972, p. 411-430. Zbl0247.47034MR295141
29. [29] M.N. Feller, On infinite dimensional elliptic operators, Sov. Math. Dokl., t. 13, n° 4, 1972, p. 890-894 (transl.). Zbl0316.47028MR326390
30. [30] H.H. Kuo, Potential theory associated with the Uhlenbeck-Ornstein process, J. Funct. Anal., t. 21, 1976, p. 63-75. Zbl0375.60087MR391285
31. [31] V. Goodman, A Liouville Theorem for abstract Wiener spaces, Amer. J. Math., t. 95, 1973, p. 215-220. Zbl0273.31012MR322971
32. [32] B. Gaveau, Intégrale stochastique radonifiante, C. R. Acad. Sci. (Paris), t. 276, 1973, p. 617-620. Zbl0256.60049MR346901
33. [33] M. Yor, Existence et unicité de diffusions à valeurs dans un espace de Hilbert. Ann. Inst. Henri Poincaré, t. 10, n° 1, 1974, p. 55-88. Zbl0281.60094MR356257
34. [34] A. Badrikian, S. Chevet, Mesures cylindriques, espaces de Wiener et fonctions aléatoires Gaussiennes, Lecture Notes in Math., 379, Springer, Berlin, 1974. Zbl0288.60009MR420760
35. [35] P. Krée, Théorie des distributions et calculs différentiels sur un espace de Banach, inSéminaire P. Lelong, 1974-1975, Lecture Notes in Math., Springer, Berlin, 1976. Zbl0334.46044MR417780
36. [36] L. Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Tata Inst., Oxford, Univ. Press, 1973. Zbl0298.28001MR426084
37. [37] S. Albeverio, R. Høegh-Krohn, L. Streit, Energy forms, Hamiltonians and distorted Brownian paths, J. Math. Phys., t. 18, 1977, p. 907-917. Zbl0368.60091MR446236

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