Duality and free measures in vector spaces, the spectral theory of actions of non-locally compact groups

DOI10.1007/s10958-019-04246-5zbMath1429.46031arXiv1709.02275OpenAlexW2963864715MaRDI QIDQ2313790

Anatoly M. Vershik

Publication date: 23 July 2019

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.02275

zbMATH Keywords

dualityspectral theoryquasi-invariant measurefree measuresvector measure space

Mathematics Subject Classification ID

Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Cites Work

• A descriptive view of unitary group representations
• Equivalence of the Brownian and energy representations
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• Factorial representations of path groups
• Measurable realizations of groups of automorphisms, and integral representations of positive operators
• Point realizations of transformation groups
• An amenable equivalence relation is generated by a single transformation
• The theory of filtrations of subalgebras, standardness, and independence
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