Related papers: Infinite measure~preserving~transformations with R…

In the following paper, we prove a dimension bound on the singular set of a Radon measure assuming its doubling ratio converges uniformly on compact sets. More precisely, we prove that if a Radon measure is $n$-Uniformly Asymptotically…

It is known that there is a comeagre set of mutually conjugate measure preserving homeomorphisms of Cantor space equipped with the coinflipping probability measure, i.e., Haar measure. We show that the generic measure preserving…

This paper describes a coplanar non invasive non destructive capacitive imaging device. We first introduce a mathematical model for its output, and discuss some of its theoretical capabilities. We show that the data obtained from this…

We focus on the irreducibility of wavelet representations. We present some connections between the following notions: covariant wavelet representations, ergodic shifts on solenoids, fixed points of transfer (Ruelle) operators and solutions…

This paper is devoted to the proof of two related results. The first one asserts that if $\mu$ is a Radon measure in $\mathbb R^d$ satisfying $$\limsup_{r\to 0} \frac{\mu(B(x,r))}{r}>0\quad \text{ and }\quad…

The conical Radon transform, which assigns to a given function $f$ on $\mathbb R^3$ its integrals over conical surfaces, arises in several imaging techniques, e.g. in astronomy and homeland security, especially when the so-called Compton…

This paper focuses on various decompositions of topological measures, deficient topological measures, signed topological measures, and signed deficient topological measures. These set functions generalize measures and correspond to certain…

Recently, M. Badger and R. Schul proved that for a $1$-rectifiable Radon measure $\mu$, the density weighted Jones' square function $$ J_{1}(x) = \mathop{\sum_{Q \in \mathcal{D}}}_{\ell(Q) \leq 1} \beta_{2,\mu}^{2}(3Q)\frac{\ell(Q)}{\mu(Q)}…

We provide an explicit construction of quasi-invariant measures on polarized coadjoint orbits of a Lie group G. The use of specific (trivial) central extensions of G by the multiplicative group ${R}^+$ allows us to restore the strict…

We study rational functions satisfying summability conditions - a family of weak conditions on the expansion along the critical orbits. Assuming their appropriate versions, we derive many nice properties: There exists a unique, ergodic, and…

We construct the first examples of genuine ergodic discrete measured groupoids that are not isomorphic to any equivalence relation or transformation groupoid. We use a construction due to B.H. Neumann of an uncountable family of pairwise…

We review recent results on Radon-Nikod\'ymification of abstract measure spaces, the particular case of integral geometric measure, and applications to the dual of SBV.

We describe the range of the Radon transform on the space $M$ of irreducible conics in $\CP^2$ in terms of natural differential operators associated to the $SO(3)$-structure on $M=SL(3, \R)/SO(3)$ and its complexification. Following…

We study a compactification of the space of invariant probability measures for a transitive countable Markov shift. We prove that it is affine homeomorphic to the Poulsen simplex. Furthermore, we establish that, depending on a combinatorial…

We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure…

We announce here a number of results concerning representation theory of the algebra $R=k<x,y>/ (xy-yx-y^2)$, known as Jordan plane (or Jordan algebra). We consider the question on 'classification' of finite-dimensional modules over the…

The note is devoted to multiple mixing, spectrum, rank and self-joinings of measure-preserving transformations. We recall famous open problems, discuss related questions and some known results. A hypothetical example of an automorphism of…

We prove an abstract Fubini-type theorem in the context of monoidal and enriched category theory, and as a corollary we establish a Fubini theorem for integrals on arbitrary convergence spaces that generalizes (and entails) the classical…

We show that, for disjoint domains in the Euclidean space whose boundaries satisfy a non-degeneracy condition, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and…

Let $G$ be a compact Lie group of Lie type $B_{n},$ such as $SO(2n+1)$. We characterize the tuples\ $(x_{1},...,x_{L})$ of the elements $x_{j}\in G$ which have the property that the product of their conjugacy classes has non-empty interior.…