Some Properties of Quasi-Invariant Measures on Groups of Diffeomorphisms of the Circle

Russian Journal of Mathematical Physics

Volumn 7, Issue 4, 2000, Pages 464-472

  Shavgulidze, E T ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034368896     PISSN: 10619208     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. Vershik, A. M., Gel'fand, I. M., and Graev, M. I., Representations of the Group of Diffeomorphisms, Uspekhi Mat. Nauk, 1975, vol. 30, no. 6 (186), pp. 1-50; English transl. in Russian Math. Surveys, 1975, vol. 30.
2. Vershik, A. M., Gel'fand, I. M., and Graev, M. I., Representations of the Group of Diffeomorphisms, Uspekhi Mat. Nauk, 1975, vol. 30, no. 6 (186), pp. 1-50; English transl. in Russian Math. Surveys, 1975, vol. 30.
3. Ismagilov, R. S., The Unitary Representations of the Group of Diffeomorphisms of a Circle, Funktsional. Anal. i Prilozhen., 1971, vol. 5, no. 3, pp. 45-53; English transl. in Functional Anal. Appl..
4. Ismagilov, R. S., The Unitary Representations of the Group of Diffeomorphisms of a Circle, Funktsional. Anal. i Prilozhen., 1971, vol. 5, no. 3, pp. 45-53; English transl. in Functional Anal. Appl..
5. Shavgulidze, E. T., A Measure That Is Quasi-Invariant with Respect to the Action of a Group of Diffeomorphisms of a Finite-Dimensional Manifold, Dokl. Akad. Nauk SSSR, 1988, vol. 303, no. 4, pp. 811-814; English transl. in Soviet Math. Dokl., 1989, vol. 38, no. 3, pp. 622-625.
6. Shavgulidze, E. T., A Measure That Is Quasi-Invariant with Respect to the Action of a Group of Diffeomorphisms of a Finite-Dimensional Manifold, Dokl. Akad. Nauk SSSR, 1988, vol. 303, no. 4, pp. 811-814; English transl. in Soviet Math. Dokl., 1989, vol. 38, no. 3, pp. 622-625.
7. Shavgulidze, E. T., An Example of a Measure Which Is Quasi-Invariant Relative to the Action of a Group of Diffeomorphims of the Circle, Funktsional. Anal. i Prilozhen., 1978, vol. 12, no. 3, pp. 55-60; English transl. in Functional. Anal. Appl..
8. Shavgulidze, E. T., An Example of a Measure Which Is Quasi-Invariant Relative to the Action of a Group of Diffeomorphims of the Circle, Funktsional. Anal. i Prilozhen., 1978, vol. 12, no. 3, pp. 55-60; English transl. in Functional. Anal. Appl..
9. Shavgulidze, E. T., Distributions on Infinite-Dimensional Spaces and Second Quantization in String Theories. II, in V Int. Vilnuis Conf. on Probability Theory and Math. Statistics, 1989, pp. 359-360.
10. Shavgulidze, E. T., Mesures quasi-invariantes sur les groupes de difféomorphismes des variétés riemaniennes, C. R. Acad. Sci. Paris Sér. I , Math., 1995, vol. 321, no. 2, pp. 229-232.
11. Shavgulidze, E. T., Mesures quasi-invariantes sur les groupes de difféomorphismes des variétés riemaniennes, Prépublication de l'Institut Fourier, n. 302, Grenoble, 1995.
12. Malliavin, M. P. and Malliavin, P., Mesures quasi invariantes sur certains groupes de dimension infinie, C. R. Acad. Sci. Paris Sér. I Math., 1990, vol. 311, no. 12, pp. 765-768.
13. Kosyak, A. V., Irreducible Regular Gaussian Representations of the Groups of the Interval and Circle Diffeomorphisms, J. Funct. Anal., 1994, vol. 125, pp. 493-547.
14. Neretin, Yu. A., Representations of Virasoro Algebra and Affine Algebras, in Sovremennye problemy matematiki. Fundamental'nye napravleniya., Moscow: VINITI, 1988, vol. 22; English transl. in Encyclopaedia of Math. Sci., vol. 22.
15. Neretin, Yu. A., Representations of Virasoro Algebra and Affine Algebras, in Sovremennye problemy matematiki. Fundamental'nye napravleniya., Moscow: VINITI, 1988, vol. 22; English transl. in Encyclopaedia of Math. Sci., vol. 22.
16. Neretin, Yu. A., Categories of Symmetries and Infinite-Dimensional Groups, Oxford: Clarendon Press, 1996.