By K. D. Elworthy (auth.), Yoshiaki Maeda, Takushiro Ochiai, Peter Michor, Akira Yoshioka (eds.)
This quantity consists of invited expository articles by way of recognized mathematicians in differential geometry and mathematical physics which were prepared in get together of Hideki Omori's fresh retirement from Tokyo collage of technology and in honor of his basic contributions to those areas.
The papers specialize in contemporary developments and destiny instructions in symplectic and Poisson geometry, international research, infinite-dimensional Lie workforce concept, quantizations and noncommutative geometry, in addition to purposes of partial differential equations and variational how you can geometry. those articles will attract graduate scholars in arithmetic and quantum mechanics, in addition to researchers, differential geometers, and mathematical physicists.
Contributors contain: M. Cahen, D. Elworthy, A. Fujioka, M. Goto, J. Grabowski, S. Gutt, J. Inoguchi, M. Karasev, O. Kobayashi, Y. Maeda, okay. Mikami, N. Miyazaki, T. Mizutani, H. Moriyoshi, H. Omori, T. Sasai, D. Sternheimer, A. Weinstein, ok. Yamaguchi, T. Yatsui, and A. Yoshioka.
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From Geometry to Quantum Mechanics: In Honor of Hideki Omori
This quantity consists of invited expository articles via recognized mathematicians in differential geometry and mathematical physics which were prepared in get together of Hideki Omori's contemporary retirement from Tokyo college of technological know-how and in honor of his basic contributions to those components.
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Roy. Soc. London Ser. A, 308(1505):523–615, 1983. S. Aida and B. K. Driver. Equivalence of heat kernel measure and pinned Wiener measure on loop groups. R. Acad. Sci. Paris S´er. , 331(9):709–712, 2000. S. Albeverio, A. Daletskii, and Y. Kondratiev. De Rham complex over product manifolds: Dirichlet forms and stochastic dynamics. In Mathematical physics and stochastic analysis (Lisbon, 1998), pages 37–53. World Sci. Publishing, River Edge, NJ, 2000. S. Aida. Stochastic analysis on loop spaces [translation of S¯ugaku 50 (1998), no.
ELa] K. D. Elworthy and Xue-Mei Li. An L 2 theory for 2-forms on path spaces I & II. In preparation. [ELb] K. D. Elworthy and Xue-Mei Li. Geometric stochastic analysis on path spaces. In Proceedings of the International Congress of Mathematicians, Madrid, 2006. Vol III, pages 575–594. European Mathematical Society, Zurich, 2006. [EL00] K. D. Elworthy and Xue-Mei Li. Special Itˆo maps and an L 2 Hodge theory for one forms on path spaces. In Stochastic processes, physics and geometry: new interplays, I (Leipzig, 1999), pages 145–162.
5, we have the following. 6 For any modified contact Weyl diffeomorphism : CU → CU which induces the identity map on the base space, there exists a Weyl function f # (ν 2 ) of the form f # (ν 2 ) = f 0 + ν 2 f +# (ν 2 ) ( f 0 ∈ R, f + (ν 2 ) ∈ C ∞ (U )[[ν 2 ]]), and smooth function g(ν 2 ) ∈ C ∞ (U )[[ν 2 ]] such that 1 = ead( ν {g(ν 2 )+ f # (ν 2 )}) (16) . 2. 7 Let Uα (resp. Uβ ) be a modified contact Weyl diffeomorphism on CUα (resp. CUβ ) inducing the identity map on the base manifold. Suppose that Uα |CUαβ = Uβ |CUβα , where Uαβ := ϕα (Vα ∩ Vβ ), Uβα := ϕβ (Vα ∩ Vβ ), CUαβ := Then −1,∗ αβ α (C Vα |Vα ∩Vβ ) (gα (ν 2 ) + ν 2 f α# (ν 2 ))|Uαβ = (gβ (ν 2 ) + ν 2 f β# (ν 2 ))|Uαβ .