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