Related papers: Paley's inequality for nonabelian groups

In this paper we study a certain recurrence relation, that can be used to generate ladder operators for the Laguerre Unitary ensemble, from the point of view of Sakai's geometric theory of Painlev\'e equations. On one hand, this gives us…

This article presents the $L^p$-Heisenberg--Pauli--Weyl uncertainty inequality for the group Fourier transform on a class of two-step nilpotent Lie groups, specifically the M\'etivier groups. This inequality quantitatively demonstrates that…

In this paper we discuss large cardinals and compactness theorems in abelian group theory. More specifically, we generalize two classical compactness results for free abelian groups to the broader context of direct sums of cyclic groups.

We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations…

In this paper we prove that if there is a regular Paley type partial difference set in an Abelian group $G$ of order $v$, where $v=p_1^{2k_1}p_2^{2k_2}\cdots p_n^{2k_n}$, $n\ge 2$, $p_1$, $p_2$, $\cdots$, $p_n$ are distinct odd prime…

We show that (with one possible exception) there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski dense.…

We formulate a version of the Pompeiu problem in the discrete group setting. Necessary and sufficient conditions are given for a finite collection of finite subsets of a discrete abelian group, whose torsion free rank is less than the…

We consider certain Littlewood-Paley operators and prove characterization of some function spaces in terms of those operators. When treating weighted Lebesgue spaces, a generalization to weighted spaces will be made for H\"ormander's…

We obtain dimension free estimates for noncommutative Riesz transforms associated to conditionally negative length functions on group von Neumann algebras. This includes Poisson semigroups, beyond Bakry's results in the commutative setting.…

We generalize a result of Sury and prove that uniform discreteness of cocompact lattices in higher rank semisimple Lie groups (first conjectured by Margulis) is equivalent to a weak form of Lehmer's conjecture. We include a short survey of…

The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its…

We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This…

We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie groups focusing on their spectral analysis. We will introduce a refined general definition of weights on the dual of locally compact groups and…

A special case of a conjecture raised by Forrest and Runde (Math. Zeit., 2005) asserts that the Fourier algebra of every non-abelian connected Lie group fails to be weakly amenable; this was aleady known to hold in the non-abelian compact…

Classical Fourier analysis has an exact counterpart in group theory and in some areas of geometry. Here I'll describe how this goes for nilpotent Lie groups and for a class of Riemannian manifolds closely related to a nilpotent Lie group…

Lie groups, and therefore Lie algebras, are fundamental structures in quantum physics that determine the space of possible trajectories of evolving systems. However, classification and characterization methods for these structures are often…

We describe a connection between the combinatorics of generators for certain groups and the combinatorics of Helly's 1913 theorem on convex sets. We use this connection to prove fixed point theorems for actions of these groups on…

Inspired by an extension of Wiener's lemma on the relation of measures $\mu$ on the unit circle and their Fourier coefficients $\widehat{\mu}(k_n)$ along subsequences $(k_n)$ of the natural numbers by Cuny, Eisner and Farkas [CEF19,…

This paper develops some general results about actions of finite groups on (infinite) abelian groups in the finite Morley rank category. They are linked to a range of problems on groups of finite Morley rank discussed in [16]. Crucially,…

We provide an operator algebraic interpretation of discrete measurable groupoids in the course of re-proving (and slightly generalizing) a result on treeability due to Adams and Spatzier. Then, we reconstruct Gaboriau's beautiful work on…