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Gaveau, Bernard; Mazet, Edmond

Opérateurs elliptiques et mesures sur l’espace des lacets invariants par le groupe des difféomorphismes du cercle. (French) Zbl 0485.58019

Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 35, 105-111 (1981).
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Cited in 2 Documents

MSC:

58J65 Diffusion processes and stochastic analysis on manifolds
58D10 Spaces of embeddings and immersions
58J70 Invariance and symmetry properties for PDEs on manifolds
58J10 Differential complexes
58D30 Applications of manifolds of mappings to the sciences

Keywords:

elliptic operator invariant by the action of diffeomorphism group; quantization by functional space integrals of the dynamics of a string; space of smooth loops of a manifold; action of the diffeomorphism group on the loop space; diffusion process on the loop space which is invariant under the action of the diffeomorphism group
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References:

[1] B. Gaveau , Intégrale stochastique radonifiante . C. R. A. S. , Paris , t. 276 , 1973 , p. 617 - 620 . MR 346901 | Zbl 0256.60049 · Zbl 0256.60049
[2] B. Gaveau , Ph. Trauber , Constructions de diffusion et de mesures invariantes par le groupe de jauge sur l’espace des connexions . Journal of functional analysis , t. 38 , 1980 , p. 324 - 341 , annoncé dans C. R. A. S. , Paris , t. 289 , 1979 , p. 609 - 612 . MR 593083 | Zbl 0451.58040 · Zbl 0451.58040 · doi:10.1016/0022-1236(80)90068-3
[3] A. Friedman , Interior estimates for parabolic systems of partial differential equations . J. of Math and Mech. , t. 7 , 1958 , p. 393 - 417 . MR 108647 | Zbl 0082.30402 · Zbl 0082.30402
[4] B. Gaveau , E. MAZET, diffusion et intégration sur les espaces de lacets . C. R. A. S. , Paris , t. 289 , 1979 , p. 643 - 646 . MR 556449 | Zbl 0426.60071 · Zbl 0426.60071
[5] B. Gaveau , Ph. Trauber , Une approche rigoureuse à la quantification du champ de Yang Mills avec cut-off . Journal of functional analysis , 1981 (à paraître) annoncé dans C. R. A. S. , Paris , t. 291 , 1980 , p. 673 - 676 . MR 604677 | Zbl 0461.60100 · Zbl 0461.60100
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