메뉴 건너뛰기




Volumn 37, Issue 1-2, 2001, Pages 15-46

Laplace operators on differential forms over configuration spaces

Author keywords

58A10; 60G57; Configuration space; Differential forms; Differential geometry; Laplace operator; Poisson measure

Indexed keywords


EID: 0002863660     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(00)00031-0     Document Type: Article
Times cited : (24)

References (37)
  • 1
    • 85031480280 scopus 로고    scopus 로고
    • Stochastic analysis on product manifolds: Dirichlet operators on differential forms
    • to appear. Preprint SFB 256 No. 598, Universität Bonn
    • S. Albeverio, A. Daletskii, Yu. Kondratiev, Stochastic analysis on product manifolds: Dirichlet operators on differential forms, J. Funct. Anal., to appear. Preprint SFB 256 No. 598, Universität Bonn, 1999.
    • (1999) J. Funct. Anal.
    • Albeverio, S.1    Daletskii, A.2    Kondratiev, Yu.3
  • 2
    • 0006923281 scopus 로고    scopus 로고
    • De Rham complex over product manifolds: Dirichlet forms and stochastic dynamics
    • in: S. Albeverio, et al. (Eds.), World Scientific, Singapore
    • S. Albeverio, A. Daletskii, Yu. Kondratiev, de Rham complex over product manifolds: Dirichlet forms and stochastic dynamics, in: S. Albeverio, et al. (Eds.), Festschrift of L. Streit, World Scientific, Singapore, 2000.
    • (2000) Festschrift of L. Streit
    • Albeverio, S.1    Daletskii, A.2    Kondratiev, Yu.3
  • 3
    • 0346013025 scopus 로고    scopus 로고
    • Laplace operators and diffusions in tangent bundles over Poisson spaces
    • in press. Preprint SFB 256 No. 629, Universität Bonn
    • S. Albeverio, A. Daletskii, E. Lytvynov, Laplace operators and diffusions in tangent bundles over Poisson spaces, Proc. KNAW, in press. Preprint SFB 256 No. 629, Universität Bonn, 1999.
    • (1999) Proc. KNAW
    • Albeverio, S.1    Daletskii, A.2    Lytvynov, E.3
  • 7
    • 0001733177 scopus 로고    scopus 로고
    • Canonical Dirichlet operator and distorted Brownian motion on Poisson spaces
    • Albeverio S., Kondratiev Yu.G., Röckner M. Canonical Dirichlet operator and distorted Brownian motion on Poisson spaces. C. R. Acad. Sci. Paris. 323:1996;1179-1184.
    • (1996) C. R. Acad. Sci. Paris , vol.323 , pp. 1179-1184
    • Albeverio, S.1    Kondratiev, Yu.g.2    Röckner, M.3
  • 9
    • 0001613648 scopus 로고    scopus 로고
    • Analysis and geometry on configuration spaces: The Gibbsian case
    • Albeverio S., Kondratiev Yu., Röckner M. Analysis and geometry on configuration spaces: the Gibbsian case. J. Funct. Anal. 157:1998;242-291.
    • (1998) J. Funct. Anal. , vol.157 , pp. 242-291
    • Albeverio, S.1    Kondratiev, Yu.2    Röckner, M.3
  • 10
    • 0033484085 scopus 로고    scopus 로고
    • Diffeomorphism groups and current algebras: Configuration spaces analysis in quantum theory
    • Albeverio S., Kondratiev Yu., Röckner M. Diffeomorphism groups and current algebras: configuration spaces analysis in quantum theory. Rev. Math. Phys. 11:1999;1-23.
    • (1999) Rev. Math. Phys. , vol.11 , pp. 1-23
    • Albeverio, S.1    Kondratiev, Yu.2    Röckner, M.3
  • 11
    • 0002130825 scopus 로고
    • Supersymmetric extension of quantum scalar field theories
    • in: H. Araki, et al. (Eds.), Kluwer Academic Publishers, Dordrecht
    • A. Arai, Supersymmetric extension of quantum scalar field theories, in: H. Araki, et al. (Eds.), Quantum and Non-commutative Analysis, Kluwer Academic Publishers, Dordrecht, 1993, pp. 73-90.
    • (1993) Quantum and Non-commutative Analysis , pp. 73-90
    • Arai, A.1
  • 12
    • 38249002029 scopus 로고
    • Dirac operators in Boson-Fermion Fock spaces and supersymmetric quantum field theory
    • Arai A. Dirac operators in Boson-Fermion Fock spaces and supersymmetric quantum field theory. J. Geom. Phys. 11:1993;465-490.
    • (1993) J. Geom. Phys. , vol.11 , pp. 465-490
    • Arai, A.1
  • 13
    • 0002298999 scopus 로고
    • De Rham-Hodge-Kodaira decomposition in ∞-dimensions
    • Arai A., Mitoma I. de Rham-Hodge-Kodaira decomposition in. ∞ -dimensions Math. Ann. 291:1991;51-73.
    • (1991) Math. Ann. , vol.291 , pp. 51-73
    • Arai, A.1    Mitoma, I.2
  • 14
    • 0347468633 scopus 로고    scopus 로고
    • Regularized Euler-Poincaré number of the infinite-dimensional torus
    • Bendikov A., Léandre R. Regularized Euler-Poincaré number of the infinite-dimensional torus. IDAQP. 2:1999;617-626.
    • (1999) IDAQP , vol.2 , pp. 617-626
    • Bendikov, A.1    Léandre, R.2
  • 16
    • 0000127272 scopus 로고
    • 2-index theorem for homogeneous spaces of Lie groups
    • 2 -index theorem for homogeneous spaces of Lie groups Ann. Math. 115:1982;291-330.
    • (1982) Ann. Math. , vol.115 , pp. 291-330
    • Connes, A.1    Moscovici, H.2
  • 18
    • 51249169618 scopus 로고
    • Non-commutative symmetric Markov semigroups
    • Davies E.B., Lindsay J.M. Non-commutative symmetric Markov semigroups. Math. Z. 210:1992;379-411.
    • (1992) Math. Z. , vol.210 , pp. 379-411
    • Davies, E.B.1    Lindsay, J.M.2
  • 20
    • 0001123307 scopus 로고
    • Geometric Aspects of Diffusions on Manifolds
    • Springer, Berlin
    • K.D. Elworthy, Geometric Aspects of Diffusions on Manifolds, Lecture Notes in Mathematics, Vol. 1362, Springer, Berlin, 1988, pp. 276-425.
    • (1988) Lecture Notes in Mathematics , vol.1362 , pp. 276-425
    • Elworthy, K.D.1
  • 21
    • 0013199023 scopus 로고    scopus 로고
    • On the Geometry of Diffusion Operators and Stochastic Flow
    • Springer, Berlin
    • K.D. Elworthy, Y. Le Jan, X.-M. Li, On the Geometry of Diffusion Operators and Stochastic Flow, Lecture Notes in Mathematics, Vol. 1720, Springer, Berlin, 1999.
    • (1999) Lecture Notes in Mathematics , vol.1720
    • Elworthy, K.D.1    Le Jan, Y.2    Li, X.-M.3
  • 23
    • 84972558081 scopus 로고
    • Hypercontractivity and logarithmic Sobolev inequalities for Clifford-Dirichlet forms
    • Gross L. Hypercontractivity and logarithmic Sobolev inequalities for Clifford-Dirichlet forms. Duke Math. J. 43:1975;383-386.
    • (1975) Duke Math. J. , vol.43 , pp. 383-386
    • Gross, L.1
  • 25
    • 0001397631 scopus 로고    scopus 로고
    • A stochastic approach to the Dirac operator over the free loop space
    • Proceedings of Steklov Institute
    • J.D.S. Jones, R. Léandre, A stochastic approach to the Dirac operator over the free loop space, in: Loop Spaces and the Group of Diffeomorphisms, Proceedings of Steklov Institute, Vol. 217, 1997, pp. 253-282.
    • (1997) In: Loop Spaces and the Group of Diffeomorphisms , vol.217 , pp. 253-282
    • Jones, J.D.S.1    Léandre, R.2
  • 27
    • 0010805441 scopus 로고
    • A stochastic approach to the Euler-Poincaré number of the loop space of developable orbifold
    • Léandre R., Roan S.S. A stochastic approach to the Euler-Poincaré number of the loop space of developable orbifold. J. Geom. Phys. 16:1995;71-98.
    • (1995) J. Geom. Phys. , vol.16 , pp. 71-98
    • Léandre, R.1    Roan, S.S.2
  • 28
    • 0001709762 scopus 로고    scopus 로고
    • Explicit stochastic analysis of Brownian motion and point measures on Riemannian manifolds
    • Prat J.J., Privault N. Explicit stochastic analysis of Brownian motion and point measures on Riemannian manifolds. J. Funct. Anal. 167:1999;201-242.
    • (1999) J. Funct. Anal. , vol.167 , pp. 201-242
    • Prat, J.J.1    Privault, N.2
  • 29
    • 0000619885 scopus 로고    scopus 로고
    • Equivalence of gradients on configuration spaces
    • Privault N. Equivalence of gradients on configuration spaces. Random Oper. Stoch. Eq. 7:1999;241-262.
    • (1999) Random Oper. Stoch. Eq. , vol.7 , pp. 241-262
    • Privault, N.1
  • 31
    • 0040745924 scopus 로고    scopus 로고
    • The convergence of the cluster expansion for continuous systems with many body interaction
    • Rebenko A.L., Shchepan'uk G.V. The convergence of the cluster expansion for continuous systems with many body interaction. J. Statist. Phys. 88:1997;665-689.
    • (1997) J. Statist. Phys. , vol.88 , pp. 665-689
    • Rebenko, A.L.1    Shchepan'Uk, G.V.2
  • 33
    • 0000030108 scopus 로고    scopus 로고
    • Stochastic analysis on configuration spaces: Basic ideas and recent results
    • in: J. Jost, et al. (Eds.), American Mathematical Society, Providence, RI
    • M. Röckner, Stochastic analysis on configuration spaces: basic ideas and recent results, in: J. Jost, et al. (Eds.), New Directions in Dirichlet Forms, Studies in Advanced Mathematics, Vol. 8, American Mathematical Society, Providence, RI, 1998, pp. 157-232.
    • (1998) New Directions in Dirichlet Forms, Studies in Advanced Mathematics , vol.8 , pp. 157-232
    • Röckner, M.1
  • 34
    • 0031995921 scopus 로고    scopus 로고
    • A support property for infinite-dimensional interacting diffusion processes
    • Röckner M., Schmuland B. A support property for infinite-dimensional interacting diffusion processes. C. R. Acad. Sci. Paris Ser. I. 326:1998;359-364.
    • (1998) C. R. Acad. Sci. Paris Ser. I , vol.326 , pp. 359-364
    • Röckner, M.1    Schmuland, B.2
  • 35
    • 84972487876 scopus 로고
    • An index theorem on open manifolds, I, II
    • 115-136
    • J. Roe, An index theorem on open manifolds, I, II, J. Differential Geom. 27 (1988) 87-113, 115-136.
    • (1988) J. Differential Geom. , vol.27 , pp. 87-113
    • Roe, J.1
  • 37
    • 0002045062 scopus 로고
    • The index of the Dirac operator in loop space
    • in: P.S. Landweber (Ed.), Lecture Notes in Mathematics, Springer, Berlin
    • W.E. Witten, The index of the Dirac operator in loop space, in: P.S. Landweber (Ed.), Elliptic Curves and Modular Forms in Algebraic Topology, Lecture Notes in Mathematics, Springer, Berlin, 1988, pp. 161-181.
    • (1988) Elliptic Curves and Modular Forms in Algebraic Topology , pp. 161-181
    • Witten, W.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.