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Creators/Authors contains: "Jamneshan, Asgar"

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  1. ; ; (, Communications of the American Mathematical Society)
    Let Γ<#comment/> \Gamma be a countable abelian group. An (abstract) Γ<#comment/> \Gamma -system X \mathrm {X} - that is, an (abstract) probability space equipped with an (abstract) probability-preserving action of Γ<#comment/> \Gamma - is said to be aConze–Lesigne systemif it is equal to its second Host–Kra–Ziegler factor Z 2 ( X ) \mathrm {Z}^2(\mathrm {X}) . The main result of this paper is a structural description of such Conze–Lesigne systems for arbitrary countable abelian Γ<#comment/> \Gamma , namely that they are the inverse limit of translational systems G n / Λ<#comment/> n G_n/\Lambda _n arising from locally compact nilpotent groups G n G_n of nilpotency class 2 2 , quotiented by a lattice Λ<#comment/> n \Lambda _n . Results of this type were previously known when Γ<#comment/> \Gamma was finitely generated, or the product of cyclic groups of prime order. In a companion paper, two of us will apply this structure theorem to obtain an inverse theorem for the Gowers U 3 ( G ) U^3(G) norm for arbitrary finite abelian groups G G . 
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  2. ; (, Ergodic Theory and Dynamical Systems)
    Abstract We prove an extension of the Moore–Schmidt theorem on the triviality of the first cohomology class of cocycles for the action of an arbitrary discrete group on an arbitrary measure space and for cocycles with values in an arbitrary compact Hausdorff abelian group. The proof relies on a ‘conditional’ Pontryagin duality for spaces of abstract measurable maps. 
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  3. ; (, Fundamenta Mathematicae)
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  4. ; (, Studia Mathematica)
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  5. ; ; ; ; ; (, Mathematische Zeitschrift)
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