Related papers: On the representation of measurable and continuous…

In this article, we generalize to the case of regular locally compact quantum groups, two important results concerning actions of compact quantum groups. Let $G_1$ and $G_2$ be two monoidally equivalent regular locally compact quantum…

Let A be a standard Borel space, and consider the space A^{\bbN^{(k)}} of A-valued arrays indexed by all size-k subsets of \bbN. This paper concerns random measures on such a space whose laws are invariant under the natural action of…

A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of…

We prove that every locally finite vertex-transitive graph $G$ admits a non-constant Lipschitz harmonic function.

We study the representations of the quantum Galilei group by a suitable generalization of the Kirillov method on spaces of non commutative functions. On these spaces we determine a quasi-invariant measure with respect to the action of the…

Let $M$ be a finite volume analytic pseudo-Riemannian manifold that admits an isometric $G$-action with a dense orbit, where $G$ is a connected non-compact simple Lie group. For low-dimensional $M$, i.e. $\dim(M) < 2\dim(G)$, when the…

Lusin's Theorem states that, for every Borel-measurable function $\bf{f}$ on $\mathbb R$ and every $\epsilon>0$, there exists a continuous function $\bf{g}$ on $\mathbb R$ which is equal to $\bf{f}$ except on a set of measure $<\epsilon$.…

We show that generalised time-frequency shifts on the Heisenberg group $\mathbf{H}_n \cong \mathbb{R}^{2n+1}$, realised as a unitary irreducible representation of a nilpotent Lie group acting on $L^{2}(\mathbf{H}_n)$, give rise to a novel…

In this paper we consider finite dimensional dynamical systems generated by a Lipschitz function. We prove a version of the Whitney's Extension Theorem on compact manifolds to obtain a version of the well-known Lambda Lemma for Lipschitz…

We consider the energy representation for the gauge group. The gauge group is the set of (C^{\infty})-mappings from a compact Riemannian manifold to a semi-simple compact Lie group. In this paper, we obtain irreducibility of the energy…

We remark a variant of the existence part of the fundamental theorem of calculus, which, together with the Lebesgue differentiation theorem, constitute a new proof that every Riemann-integrable function on a compact interval having limit…

The main result of the present paper is a Rademacher-type theorem for intrinsic Lipschitz graphs of codimension $k\leq n$ in sub-Riemannian Heisenberg groups $\mathbb H^n$. For the purpose of proving such a result we settle several related…

We generalize an equidistribution theorem \`a la Bader-Muchnik for operator-valued measures constructed from a family of boundary representations associated with Gibbs measures in the context of convex cocompact discrete group of isometries…

On complete metric spaces that support doubling measures, we show that the validity of a Rademacher theorem for Lipschitz functions can be characterised by Keith's "Lip-lip" condition. Roughly speaking, this means that at almost every…

In his 1951 book "Infinite Abelian Groups", Kaplansky gives a combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group. In this paper we first use partial maps on…

Let $G$ be a compact abelian group, let $\mu$ be the corresponding Haar measure, and let $\hat G$ be the Pontryagin dual of $G$. Further, let $C_p$ denote the Schatten class of operators on some separable infinite dimensional Hilbert space,…

We study the well-posedness and the long-time behavior of almost periodic solutions to stochastic degenerate parabolic-hyperbolic equations in any space dimension, under the assumption of Lipschitz continuity of the flux and viscosity…

The intent of this short note is to extend real valued Lipschitz functions on metric spaces, while locally preserving the asymptotic Lipschitz constant. We then apply this results to give a simple and direct proof of the fact that Sobolev…

Using a recent Furstenberg structure theorem, we obtain Multiple Recurrence Theorems relative to any locally compact second countable Noetherian module $G$ over a syndetic ring $R$, which generalizes Furstenberg's multiple recurrence…

In this paper we connect the well established discrete frame theory of generalized shift invariant systems to a continuous frame theory. To do so, we let $\Gamma_j$, $j \in J$, be a countable family of closed, co-compact subgroups of a…