Properties of quasi-invariant measures on topological groups and associated algebras

S.V. Ludkovsky

S.V. Ludkovsky

Annales mathématiques Blaise Pascal, Tome 6 (1999) no. 1, pp. 33-45

MR Zbl

@article{AMBP_1999__6_1_33_0,
     author = {S.V. Ludkovsky},
     title = {Properties of quasi-invariant measures on topological groups and associated algebras},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {33--45},
     publisher = {Laboratoires de Math\'ematiques Pures et Appliqu\'ees de l'Universit\'e Blaise Pascal},
     volume = {6},
     number = {1},
     year = {1999},
     zbl = {0936.22004},
     mrnumber = {1693126},
     language = {en},
     url = {https://ambp.centre-mersenne.org/item/AMBP_1999__6_1_33_0/}
}

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S.V. Ludkovsky. Properties of quasi-invariant measures on topological groups and associated algebras. Annales mathématiques Blaise Pascal, Tome 6 (1999) no. 1, pp. 33-45. https://ambp.centre-mersenne.org/item/AMBP_1999__6_1_33_0/

Bibliographie
Cité par

[1] N. Bourbaki. Lie groups and algebras (Moscow: Mir, 1976). | MR

[2] Yu.L. Dalecky, S.V. Fomin. Measures and differential equations in infinite-dimensional space (Kluwer: Dordrecht, The Netherlands, 1991). | Zbl

[3] Yu.L. Daletskii, Ya.I. Shnaiderman . Diffusion and quasi-invariant measures on infinite-dimensional Lie groups. Funct. Anal. and its Applications. 3 (1969), 156-158.

[4] R. Engelking. General topology (Moscow: Mir,1986). | MR

[5] H. Federer. Geometric measure theory(Berlin:Springer-Verlag, 1969). | Zbl | MR

[6] J.M.G. Fell, R.S. Doran. Representations of *-algebras. locally compact groups, and Banach *-algebraic bundles (Acad. Pr.: Boston, 1988). | Zbl

[7] E. Hewitt and K.A. Ross. Abstract harmenic analysis. Second edition (Berlin: Springer-Verlag, 1979). | MR

[8] A.V. Kosyak. Irreducible Gaussian representations of the group of the interval and circle diffeomorphisms. J. Funct. Anal. 125(1994), 493-547. | Zbl | MR

[9] H.-H. Kuo. Gaussian measures in Banach spaces (Springer, Berlin, 1975). | Zbl | MR

[10] S.V. Ludkovsky. Measures on groups of diffeomorphisms of non-Archimedean Banach manifolds, Usp. Mat. Nauk. 51(1996), 169-170 (N° 2). | Zbl | MR

[11] S.V. Ludkovsky. Measurability of repesentations of locally compact groups. Math. Sb. 186 1995, 83-92 (N°2). | Zbl | MR

[12] S.V. Ludkovsky. Measures on groups of diffeomorphisms of non-Archimedean manifolds, representations of groups and their applications. Theoret. i Mathem. Phys., 1999.

[13] S.V. Ludkovsky. Quasi-invariant measures on non-Archimedean semigroups of loops. Usp. Mat. Nauk, 53 (1998), 203-204 (N° 3). | Zbl | MR

[14] S.V. Ludkovsky. Quasi-invariant measures on a group of diffeomorphisms of an infinite-dimensional real manifold and induced irreducible unitary representations. Rendiconti dell'Istituto di Matematica dell'Università di Trieste. Nuova Serie. 26 pages, is accepted for publication, 1999. | Zbl

[15] S.V. Ludkovsky. Quasi-invariant measures on loop groups of Riemann manifolds. Dokl. Ross. Acad. Nauk, to appear.

[16] S.V. Ludkovsky. Gaussian quasi-invariant measures on loop groups and semigroups of real manifolds and their representations. IHES, Bures, France, preprint IHES/M/97/95.

[17] S.V. Ludkovsky. Quasi-invariant measures on non-Archimedean groups and semigroups of loops and paths, their representations. IHES/M/98/36.

[18] S.V. Ludkovsky. Quasi-invariant measures on groups of diffeomorphisms of Schwarz class of smoothness for real manifolds. IHES/M/97/96.

[19] S.V. Ludkovsky. Quasi-invariant and pseudo-differentiable measures on a non-Archimedean Banach space. Intern. Centre for Theoret. Phys. Trieste, Italy. Preprint (http://www.ictp.trieste.it) IC/96/210, October 1996.

[20] S.V. Ludkovsky. Quasi-invariant measures on a non-Archimedean group of diffeomorphisms and on a Banach manifold. ICTP. IC/96/215, October, 1996.

[21] S.V. Ludkovsky. Quasi-invariant measures on groups of diffeomorphisms of real Banach manifolds. ICTP. IC/96/218, October, 1996.

[22] M.A. Naimark. Normed rings (Moscow: Nauka, 1968). | MR

[23] Yu.A. Neretin. Representations of the Virasoro algebra and affine algebras. in: Itogi Nauki i Tech. Ser. Sovr. Probl. Math. Fund. Napravl(Moscow: Nauka) 22(1988), 163-230. | Zbl | MR

[24] E.T. Shavgulidze. About one measure quasi-invariant relative to an action of a diffeomorphisms group of a finite-dimensional manifold. Dokl. Akad. Nauk SSSR. 303(1988), 811-814. | Zbl | MR

[25] A.V. Skorohod. Integration in the Hilbert space (Moscow: Nauka, 1975).