On circle diffeomorphisms with discontinuous derivatives and quasi-invariance subgroups of Malliavin-Shavgulidze measures |
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Authors: | P.A. Kuzmin |
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Affiliation: | Department of Physics, Moscow State University, Leninskie gory, Moscow 119899, Russia |
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Abstract: | This note is devoted to construction of the domain of the regular representation of Diff+(S1). We consider a subgroup of diffeomorphism group such that the Malliavin-Shavgulidze measure is quasi-invariant with respect to the left action of the subgroup. The measure appears to be quasi-invariant with respect to the left action of diffeomorphisms with discontinuous second derivative. We derive an expression for quasi-invariance density and obtain an additional PSL(2,R) symmetry breaking term. |
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Keywords: | Diffeomorphism group Quasi-invariant measure Regular representation |
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