The maximum Markovian self-adjoint extensions of generalized Schrödinger operators

Masayoshi TAKEDA

doi:10.2969/jmsj/04410113

Masayoshi TAKEDA

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JOURNAL FREE ACCESS

1992 Volume 44 Issue 1 Pages 113-130

DOI https://doi.org/10.2969/jmsj/04410113

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Published: 1992 Received: July 20, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. A. Adams, Sobolev Spaces, Academic Press, 1975.
2) S. Albeverio, M. Fukushima, W. Karwowski and L. Streit, Capacity and Quantum Mechanical Tunneling, Commun. Math. Phys., 81 (1981), 501-513.
3) S. Albeverio, F. Gesztesy, W. Karwowski and L. Streit, On the connection between Schrödinger and Dirichlet forms, J. Math. Phys., 26 (1985), 2546-2553.
4) S. Albeverio, R. Høegh-Krohn and L. Streit, Energy forms, Hamiltonians, and distorted Brownian paths, J. Math. Phys., 18 (1977), 907-917.
5) S. Albeverio and S. Kusuoka, Maximality of infinite dimensional Dirichlet forms and Høegh-Krohn's model of quantum fields, Kyoto-Bochum, preprint.
6) S. Albeverio and M. Röckner, On Dirichlet forms on topological vector spaces; existence and maximality, To appear in Proc. Bad-Honnef Conference, ed. N. Christopeit et al.
7) G. Allian, Sur la representation des forms de Dirichlet, Ann. Inst. Fourier, 25 (1975), 1-10.
8) M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland, Kodansha, 1980.
9) M. Fukushima, On Dirichlet spaces and Dirichlet rings, Proc. Japan Acad., 45 (1969), 433-436.
10) M. Fukushima, Regular representations of Dirichlet spaces, Trans. Amer. Math. Soc., 155 (1971), 455-473.
11) M. Fukushima and M. Takeda, A transformation of a symmetric Markov process and the Donsker-Varadhan theory, Osaka J. Math., 21 (1984), 311-326.
12) K. Ito and H. P. Mckean, Diffusion processes and their sample paths, Springer-Verlag, 1965.
13) A. Kufner, Weighted Sobolev Spaces, John Wiley & Sons, 1985.
14) M. M. H. Pang, L¹-properties of two classes of singular second order elliptic operators, J. London Math. Soc., 38 (1988), 525-543.
15) M. Reed and B. Simon, Methods of Modern Mathematical physics II, Academic Press, 1975.
16) M. Röckner and N. Wielens, Dirichlet forms-closability and change of speed measures, Infinite Dimensional Analysis and Stochastic Processes, ed. S. Albeverio, Pitman, London, 1985, pp. 119-144.
17) M. Takeda, On the uniqueness of Markovian self-adjoint extension of diffusion operators on infinite dimensional spaces, Osaka J. Math., 22 (1985), 733-742.
18) N. Wielens, The essential self-adjointness of generalized Schrödinger operators, J. Func. Anal., 61 (1985), 98-115.

Right : [1] R. A. Adams, Sobolev Spaces, Academic Press, 1975.
[2] S. Albeverio, M. Fukushima, W. Karwowski and L. Streit, Capacity and Quantum Mechanical Tunneling, Commun. Math. Phys., 81 (1981), 501-513.
[3] S. Albeverio, F. Gesztesy, W. Karwowski and L. Streit, On the connection between Schrödinger and Dirichlet forms, J. Math. Phys., 26 (1985), 2546-2553.
[4] S. Albeverio, R. Høegh-Krohn and L. Streit, Energy forms, Hamiltonians, and distorted Brownian paths, J. Math. Phys., 18 (1977), 907-917.
[5] S. Albeverio and S. Kusuoka, Maximality of infinite dimensional Dirichlet forms and Høegh-Krohn's model of quantum fields, Kyoto-Bochum, preprint.
[6] S. Albeverio and M. Röckner, On Dirichlet forms on topological vector spaces; existence and maximality, To appear in Proc. Bad-Honnef Conference, ed. N. Christopeit et al.
[7] G. Allian, Sur la representation des forms de Dirichlet, Ann. Inst. Fourier, 25 (1975), 1-10.
[8] M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland, Kodansha, 1980.
[9] M. Fukushima, On Dirichlet spaces and Dirichlet rings, Proc. Japan Acad., 45 (1969), 433-436.
[10] M. Fukushima, Regular representations of Dirichlet spaces, Trans. Amer. Math. Soc., 155 (1971), 455-473.
[11] M. Fukushima and M. Takeda, A transformation of a symmetric Markov process and the Donsker-Varadhan theory, Osaka J. Math., 21 (1984), 311-326.
[12] K. Ito and H. P. Mckean, Diffusion processes and their sample paths, Springer-Verlag, 1965.
[13] A. Kufner, Weighted Sobolev Spaces, John Wiley & Sons, 1985.
[14] M. M. H. Pang, L¹-properties of two classes of singular second order elliptic operators, J. London Math. Soc., 38 (1988), 525-543.
[15] M. Reed and B. Simon, Methods of Modern Mathematical physics II, Academic Press, 1975.
[16] M. Röckner and N. Wielens, Dirichlet forms-closability and change of speed measures, Infinite Dimensional Analysis and Stochastic Processes, ed. S. Albeverio, Pitman, London, 1985, pp. 119-144.
[17] M. Takeda, On the uniqueness of Markovian self-adjoint extension of diffusion operators on infinite dimensional spaces, Osaka J. Math., 22 (1985), 733-742.
[18] N. Wielens, The essential self-adjointness of generalized Schrödinger operators, J. Func. Anal., 61 (1985), 98-115.

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