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Volumn 27, Issue 1, 1998, Pages 69-91

Strong Uniqueness for Certain Infinite Dimensional Dirichlet Operators and Applications to Stochastic Quantization

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EID: 85129557881     PISSN: 0391173X     EISSN: 20362145     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (26)

References (46)
  • 1
    • 0001538820 scopus 로고
    • An approximate criterium of essential self-adjointness ofDirichlet operators
    • S. ALBEVERIO - YU.G. KONDRATIEV - M . RÖCKNER, An approximate criterium of essential self-adjointness ofDirichlet operators. Potential Anal. 1 (1992), 307-317.
    • (1992) Potential Anal , vol.1 , pp. 307-317
    • ALBEVERIO, S.1    KONDRATIEV, YU.G.2    RÖCKNER, M .3
  • 2
    • 0347878598 scopus 로고
    • Addendum to: An approximate criterium of essential self-adjointness ofDirichlet operators
    • S. ALBEVERIO - Y . G . KONDRATIEV - M . RÖCKNER, Addendum to: An approximate criterium of essential self-adjointness ofDirichlet operators. Potential A n a l. 2 (1993), 195-198.
    • (1993) Potential A n a l , vol.2 , pp. 195-198
    • ALBEVERIO, S.1    KONDRATIEV, Y . G .2    RÖCKNER, M .3
  • 4
    • 0010880898 scopus 로고    scopus 로고
    • Ergodicity for the stochastic dynamics ofquasi-invariant measures with applications to Gibbs states
    • SFB-343-Preprint To appear in
    • S. ALBEVERIO - Y U . G . KONDRATIEV - M . KÖCKNER, Ergodicity for the stochastic dynamics ofquasi-invariant measures with applications to Gibbs states. SFB-343-Preprint 1996, To appear in: J. Funct. Anal.
    • (1996) J. Funct. Anal
    • ALBEVERIO, S.1    KONDRATIEV, Y U . G .2    KÖCKNER, M .3
  • 5
    • 0000079939 scopus 로고
    • Dirichletforms on topological vector spaces-construction ofan associated diffusion process
    • S. ALBEVERIO - M . RÖCKNER, Dirichletforms on topological vector spaces-construction ofan associated diffusion process, Probab. Theory Related Fields 83 (1989), 405-434.
    • (1989) Probab. Theory Related Fields , vol.83 , pp. 405-434
    • ALBEVERIO, S.1    RÖCKNER, M .2
  • 6
    • 0039561025 scopus 로고
    • Dirichlet forms, quantum fields and stochastic quantization. Stochastic analysis, path integration and dynamics
    • Editors: K. D. Elworthy, J. C. Zambrini. Harlow: Longman
    • S. ALBEVERIO - M . RÖCKNER, "Dirichlet forms, quantum fields and stochastic quantization. Stochastic analysis, path integration and dynamics". Research Notes in Mathematics, vol. 200, 1-21. Editors: K. D. Elworthy, J. C. Zambrini. Harlow: Longman 1989.
    • (1989) Research Notes in Mathematics , vol.200 , pp. 1-21
    • ALBEVERIO, S.1    RÖCKNER, M .2
  • 7
    • 0000765766 scopus 로고
    • Classical Dirichletforms on topological spaces-Closability and Cameron-Martinformula
    • S. ALBEVERIO - M. RÖCKNER, Classical Dirichletforms on topological spaces-Closability and Cameron-Martinformula, J. Funct. Anal. 88 (1990), 395-436.
    • (1990) J. Funct. Anal , vol.88 , pp. 395-436
    • ALBEVERIO, S.1    RÖCKNER, M.2
  • 8
    • 0000364933 scopus 로고
    • Stochastic differential equations in infinite dimensions: solutions via Dirichletforms
    • S. ALBEVERIO - M. RÖCKNER, Stochastic differential equations in infinite dimensions: solutions via Dirichletforms, Probab. Theory Related Fields 89 (1991), 347-386.
    • (1991) Probab. Theory Related Fields , vol.89 , pp. 347-386
    • ALBEVERIO, S.1    RÖCKNER, M.2
  • 9
    • 0000937874 scopus 로고
    • Girsanov transform for symmetric diffusions with infinite dimensional state space
    • S. ALBEVERIO - M. RÖCKNER - T . S. ZHANG, Girsanov transform for symmetric diffusions with infinite dimensional state space., Ann. Probab. 21 (1993), 961-978.
    • (1993) Ann. Probab , vol.21 , pp. 961-978
    • ALBEVERIO, S.1    RÖCKNER, M.2    ZHANG, T . S.3
  • 10
    • 0001801736 scopus 로고
    • Markov uniqueness and its applications to martingale problems, stochastic differential equations and stochastic quantization
    • S. ALBEVERIO - M . RÖCKNER - T . S. ZHANG, Markov uniqueness and its applications to martingale problems, stochastic differential equations and stochastic quantization, C.R. Math. Rep. Acad. Sci. Canada XV (1993), 1-6.
    • (1993) C.R. Math. Rep. Acad. Sci. Canada , vol.XV , pp. 1-6
    • ALBEVERIO, S.1    RÖCKNER, M .2    ZHANG, T . S.3
  • 14
    • 0039602124 scopus 로고
    • Stochastic quantization of fie Id theory in finite and infinite volume
    • V.S. BORKAR - R.T. CHARI - S.K . MITTER, Stochastic quantization of fie Id theory in finite and infinite volume, J. Funct. Anal. 81 (1988), 184-206.
    • (1988) J. Funct. Anal , vol.81 , pp. 184-206
    • BORKAR, V.S.1    CHARI, R.T.2    MITTER, S.K .3
  • 16
    • 0003939017 scopus 로고
    • Cambridge University Press, Cambridge-New York-New Rochelle-Melboume-Sydney
    • E.B. DAVIES, "Heat Kernels and Spectral Theory", Cambridge University Press, Cambridge-New York-New Rochelle-Melboume-Sydney, 1989.
    • (1989) Heat Kernels and Spectral Theory
    • DAVIES, E.B.1
  • 23
    • 0000945929 scopus 로고
    • On the stochastic quantization of field theory
    • G. JONA-LASINIO - P. K . MITTER, On the stochastic quantization of field theory. Comm. Math. Phys. 101 (1985), 406-436.
    • (1985) Comm. Math. Phys , vol.101 , pp. 406-436
    • JONA-LASINIO, G.1    MITTER, P. K .2
  • 24
    • 0000191314 scopus 로고
    • Large deviation estimates in the stochastic quantization of^\
    • G. JONA-LASINIO - P. K . MITTER, Large deviation estimates in the stochastic quantization of^\. Comm. Math. Phys. 130 (1990), 111-121.
    • (1990) Comm. Math. Phys , vol.130 , pp. 111-121
    • JONA-LASINIO, G.1    MITTER, P. K .2
  • 25
    • 0038952850 scopus 로고
    • On a class ofstochastic reaction-diffusion equations in two space dimensions
    • G. JONA-LASINIO - R. SENEOR, On a class ofstochastic reaction-diffusion equations in two space dimensions, J. Phys. A 24 (1991), 4123-4128.
    • (1991) J. Phys. A , vol.24 , pp. 4123-4128
    • JONA-LASINIO, G.1    SENEOR, R.2
  • 26
    • 0003807870 scopus 로고    scopus 로고
    • Lectures on elliptic and parabolic equations in Holder spaces
    • American Mathematical Society
    • N. V. KRYLOV, "Lectures on elliptic and parabolic equations in Holder spaces". Graduate Studies in Mathematics, Vol. 12. American Mathematical Society, 1996.
    • (1996) Graduate Studies in Mathematics , vol.12
    • KRYLOV, N. V.1
  • 27
    • 0003575867 scopus 로고
    • Non-homogeneous boundary value problems and applications
    • Berlin: Springer
    • J . L . LIONS - E . M AGENES. Non-homogeneous boundary value problems and applications, in: Grundlehren Math. Wiss., Berlin: Springer, 1972.
    • (1972) Grundlehren Math. Wiss
    • LIONS, J . L .1    AGENES, E . M2
  • 29
    • 0042476048 scopus 로고
    • Smoothness estimates and uniqueness for the Dirichlet operator
    • V. A. LiSKEViCH, Smoothness estimates and uniqueness for the Dirichlet operator, in: Operator Theory: Advances and AppHcations 70 (1994), 149-152.
    • (1994) Operator Theory: Advances and AppHcations , vol.70 , pp. 149-152
    • LiSKEViCH, V. A.1
  • 30
    • 38249010161 scopus 로고
    • Dirichlet operators: a priori estimates and the uniqueness problem
    • V. A. LiSKEViCH - Yu . A. SEMENOV, Dirichlet operators: a priori estimates and the uniqueness problem, J. Funct. Anal. 109 (1992), 199-213.
    • (1992) J. Funct. Anal , vol.109 , pp. 199-213
    • LiSKEViCH, V. A.1    SEMENOV, Yu . A.2
  • 32
    • 85129522940 scopus 로고    scopus 로고
    • Martingale problemsfor stochastic PDE's
    • Preprint To appear in: Stochastic partial differential equations: Six Perspectives. Editors: R. Cannona, B. L. Rozowski. AMS Series Monographs and Reviews
    • R. MiKULEVicius - B. I. RozowsKi, Martingale problemsfor stochastic PDE's. Preprint (1997), To appear in: Stochastic partial differential equations: Six Perspectives. Editors: R. Cannona, B. L. Rozowski. AMS Series Monographs and Reviews.
    • (1997)
    • MiKULEVicius, R.1    RozowsKi, B. I.2
  • 33
    • 0040746424 scopus 로고
    • Stochastic approach to Euclidean field theory (Stochastic quantization)
    • Editors: J. Abad, M. Asorey, A. Cruz. Singapore: World Scientific
    • P. K . MITTER, Stochastic approach to Euclidean field theory (Stochastic quantization), in: New perspectives in Quantum Field Theory. Editors: J. Abad, M. Asorey, A. Cruz. Singapore: World Scientific, 1986.
    • (1986) New perspectives in Quantum Field Theory
    • MITTER, P. K .1
  • 34
    • 0004011167 scopus 로고
    • One-Parameter Semigroups of Positive Operators
    • (editor), Springer-Verlag, Berlin-Heidelberg-New York
    • R. NAGEL (editor), "One-Parameter Semigroups of Positive Operators", Lecture Notes in mathematics 1184, Springer-Verlag, Berlin-Heidelberg-New York, 1986.
    • (1986) Lecture Notes in mathematics , vol.1184
    • NAGEL, R.1
  • 35
    • 49549166117 scopus 로고
    • The free Markov field
    • E . NELSON, The free Markov field, J . Funct. Anal. 12 (1973), 211-227.
    • (1973) J . Funct. Anal , vol.12 , pp. 211-227
    • NELSON, E .1
  • 36
    • 0001562027 scopus 로고
    • Perturbation theory without gauge fixing
    • G. PARISI - Y . S. Wu, Perturbation theory without gauge fixing, Scienta Sinica 24 (1981), 383-496.
    • (1981) Scienta Sinica , vol.24 , pp. 383-496
    • PARISI, G.1    Wu, Y . S.2
  • 37
    • 0003687441 scopus 로고
    • Methods of Modem Mathematical Physics I V
    • Orlando, F L: Academic Press
    • M. REED - B . SIMON, "Methods of Modem Mathematical Physics I V ", Analysis of Operators. Orlando, F L: Academic Press, 1978.
    • (1978) Analysis of Operators
    • REED, M.1    SIMON, B .2
  • 38
    • 0010824457 scopus 로고
    • Specifications andMartin boundariesfor P ((p)2-random fields
    • M. RÖCKNER, Specifications andMartin boundariesfor P ((p)2-random fields. Comm. Math. Phys. 106 (1986), 105-135.
    • (1986) Comm. Math. Phys , vol.106 , pp. 105-135
    • RÖCKNER, M.1
  • 39
    • 0000327833 scopus 로고
    • On uniqueness of generalized Schrödinger operators and applications
    • M. RÖCKNER - T.-S. ZHANG, On uniqueness of generalized Schrödinger operators and applications, J. Funct. Anal. 105 (1992), 187-231.
    • (1992) J. Funct. Anal , vol.105 , pp. 187-231
    • RÖCKNER, M.1    ZHANG, T.-S.2
  • 40
    • 0001390366 scopus 로고
    • Uniqueness of generalized Schrödinger operators and applications II
    • M. RÖCKNER - T.-S. ZHANG, Uniqueness of generalized Schrödinger operators and applications II, J. Funct. Anal. 119 (1994), 455-467.
    • (1994) J. Funct. Anal , vol.119 , pp. 455-467
    • RÖCKNER, M.1    ZHANG, T.-S.2
  • 41
    • 0008980670 scopus 로고    scopus 로고
    • Finite dimensional approximation ofdiffusion processes on infinite dimensional state spaces
    • M. RÖCKNER - T . S. ZHANG, Finite dimensional approximation ofdiffusion processes on infinite dimensional state spaces, Stochastics Stochastics Rep. 57 (1996), 37-55.
    • (1996) Stochastics Stochastics Rep , vol.57 , pp. 37-55
    • RÖCKNER, M.1    ZHANG, T . S.2
  • 42
    • 21344460443 scopus 로고
    • An example of regular (r, p)-capacity and essential self-adjointness of a diffusion operator in infinite dimensions
    • I . SHIGEKAWA, An example of regular (r, p)-capacity and essential self-adjointness of a diffusion operator in infinite dimensions, J. Math. Kyoto Univ. 35 (1995), 639-651.
    • (1995) J. Math. Kyoto Univ , vol.35 , pp. 639-651
    • SHIGEKAWA, I .1
  • 45
    • 0039493406 scopus 로고
    • On the essential self-adjointness of generalized Schrödinger operators
    • N . WIELENS, On the essential self-adjointness of generalized Schrödinger operators, J . Funct. Anal. 61 (1985), 98-115.
    • (1985) J . Funct. Anal , vol.61 , pp. 98-115
    • WIELENS, N .1
  • 46
    • 80052515834 scopus 로고
    • Generalizations of Gross' and Minios' theorems
    • (J. Azema et. al), Lect. Notes in Math. 1372. Beriin: Springer
    • J.A. YAN, "Generalizations of Gross' and Minios' theorems", in: Séminaire de Probabilités XXII, (J. Azema et. al.), 395-404, Lect. Notes in Math. 1372. Beriin: Springer, 1989.
    • (1989) Séminaire de Probabilités XXII , pp. 395-404
    • YAN, J.A.1


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