O. Shalom

activity

20202026

most citedMultiple ergodic averages in abelian groups and Khintchine type recurrence

14 citations · 30 across the 16 of their papers we have counts for

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Showing 2023Show all

4 papers · 1 filter

math.DS2023

On the maximal spectral type of nilsystems

Ethan Ackelsberg, Florian K. Richter, Or Shalom

Let $(G /Γ, R_{a})$ be an ergodic $k$ -step nilsystem for $k \geq 2$ . We adapt an argument of Parry to show that $L^{2} (G /Γ)$ decomposes as a sum of a subspace with discrete spectrum and a…

math.DS2023

The structure of totally disconnected Host--Kra--Ziegler factors, and the inverse theorem for the $U^{k}$ Gowers uniformity norms on finite abelian groups of bounded torsion

Asgar Jamneshan, Or Shalom, Terence Tao

Let $Γ$ be a countable abelian group, let $k \geq 1$ , and let $X = (X, X, μ, T)$ be an ergodic $Γ$ -system of order $k$ in the sense of Host--Kra--Ziegler. The $Γ$ -syst…

math.DS2023

A Host--Kra $F_{2}^{ω}$ -system of order $5$ that is not Abramov of order $5$ , and non-measurability of the inverse theorem for the $U^{6} (F_{2}^{n})$ norm

Asgar Jamneshan, Or Shalom, Terence Tao

It was conjectured by Bergelson, Tao, and Ziegler \cite{btz} that every Host--Kra $\F_p^ω$-system of order $k$ is an Abramov system of order $k$ . This conjecture has been verified…

math.DS2023

The structure of non-commutative multiple correlation sequences and applications

Or Shalom

Let $Γ$ be a countable abelian group with Pontryagin dual $Σ := Γ$ . A non-commutative $2$ -fold multiple correlation sequence is a double-indexed sequence $$b(γ,γ') = \int_X T…

On the maximal spectral type of nilsystems

The structure of totally disconnected Host--Kra--Ziegler factors, and the inverse theorem for the Uk Gowers uniformity norms on finite abelian groups of bounded torsion

A Host--Kra F2ω​-system of order 5 that is not Abramov of order 5, and non-measurability of the inverse theorem for the U6(F2n​) norm

The structure of non-commutative multiple correlation sequences and applications

The structure of totally disconnected Host--Kra--Ziegler factors, and the inverse theorem for the $U^{k}$ Gowers uniformity norms on finite abelian groups of bounded torsion

A Host--Kra $F_{2}^{ω}$ -system of order $5$ that is not Abramov of order $5$ , and non-measurability of the inverse theorem for the $U^{6} (F_{2}^{n})$ norm