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Quasi-invariant measures on sets of piecewise smooth homeomorphisms of closed intervals and circles and representations of diffeomorphism groups

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Abstract

Families of measures are constructed that are quasi-invariant with respect to the action of C 1-diffeomorphisms, for a closed interval and a circle, and have bounded Borel measurable second derivatives. A series of pairwise nonequivalent irreducible representations of the group of C 3-diffeomorphisms of the circle is introduced on the space of functions that are square integrable against these measures.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University, 119992, GSP-2, Moscow, Russia

    A. A. Dosovitskii

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  1. A. A. Dosovitskii
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Correspondence to A. A. Dosovitskii.

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Dosovitskii, A.A. Quasi-invariant measures on sets of piecewise smooth homeomorphisms of closed intervals and circles and representations of diffeomorphism groups. Russ. J. Math. Phys. 18, 258–296 (2011). https://doi.org/10.1134/S1061920811030022

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