Related papers: On the support of measures in multiplicative free …

We study the structure of invariant measures for continuous automorphisms of compact metrizable abelian groups satisfying the descending chain condition. We show that the finitely supported invariant measures are weak-* dense in the space…

Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the…

We realize the Belinschi-Nica semigroup of homomorphisms as a free multiplicative subordination. This realization allows to define more general semigroups of homomorphisms with respect to free multiplicative convolution. For these…

We study (weakly) continuous convolution semigroups of probability measures on a Lie group G or a homogeneous space G/K, where K is a compact subgroup. We show that such a convolution semigroup is the convolution product of its initial…

The wrapping transformation $W$ is a homomorphism from the semigroup of probability measures on the real line, with the convolution operation, to the semigroup of probability measures on the circle, with the multiplicative convolution…

We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of…

We prove that the free additive convolution of two Borel probability measures supported on the real line can have a component that is singular continuous with respect to the Lebesgue measure on the real line only if one of the two measures…

In [6], a constraint on invariant measures of bi-permutative cellular automata has been observed: fixed values at the positive indices determine almost-surely a uniform conditional probability on the subset of values of positive conditional…

For discrete measured groupoids preserving a probability measure we introduce a notion of sofic dimension that measures the asymptotic growth of the number of sofic approximations on larger and larger finite sets. In the case of groups we…

We introduce notions of absolutely continuous functionals and representations on the non-commutative disk algebra $A_n$. Absolutely continuous functionals are used to help identify the type L part of the free semigroup algebra associated to…

We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…

Endomorphisms of the measure algebra of commutative hypergroups are investigated. We focus on derivations and higher order derivations which are closely related to moment function sequences of higher rank. We describe the exact connection…

The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…

Consider a sequence of linear contractions $S_{j}(x)=\varrho x+d_{j}$ and probabilities $p_{j}>0$ with $\sum p_{j}=1$. We are interested in the self-similar measure $\mu =\sum p_{j}\mu \circ S_{j}^{-1}$, of finite type. In this paper we…

We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…

For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant…

In his article "On the free convolution with a semicircular distribution," Biane found very useful characterizations of the boundary values of the imaginary part of the Cauchy-Stieltjes transform of the free additive convolution of a…

We study the freely infinitely divisible distributions that appear as the laws of free subordinators. This is the free analog of classically infinitely divisible distributions supported on [0,\infty), called the free regular measures. We…

Let $\mu$ be a positive measure on the real line with locally finite support $\Lambda$ and integer masses such that its Fourier transform in the sense of distributions is a purely point measure. An explicit form is found for an entire…

This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…