Irreducible regular Gaussian representations of the groups of the interval and circle diffeomorphisms

DOI10.1006/jfan.1994.1135zbMath0829.22032OpenAlexW1973960815MaRDI QIDQ1340839

Alexander V. Kosyak

Publication date: 20 December 1994

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1994.1135

zbMATH Keywords

Wiener measureregular representationMalliavin measureShavgulidze measure

Mathematics Subject Classification ID

Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

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Criteria of irreducibility of the Koopman representations for the group \(\mathrm{GL}_0(2\infty,\mathbb R)\) ⋮ Topological transformation groups of manifolds over non-Archimedean fields, their representations, and quasi-invariant measures. I. ⋮ On circle diffeomorphisms with discontinuous derivatives and quasi-invariance subgroups of Malliavin-Shavgulidze measures ⋮ Quasi-invariant measures on sets of piecewise smooth homeomorphisms of closed intervals and circles and representations of diffeomorphism groups ⋮ Induced representations of infinite-dimensional groups. I. ⋮ Some measures on the set of piecewise smooth circle homeomorphisms and related representations of the circle diffeomorphism group ⋮ Quasiregular representations of the infinite-dimensional Borel group ⋮ Quasiregular representations of the infinite-dimensional nilpotent group ⋮ Inversion quasi-invariant Gaussian measures on the group of upper-triangular matrices of infinite order ⋮ Properties of quasi-invariant measures on topological groups and associated algebras

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