Related papers: The moment problem with bounded density

We address some usually overlooked issues concerning the use of $*$-algebras in quantum theory and their physical interpretation. If $\mathfrak{A}$ is a $*$-algebra describing a quantum system and $\omega\colon\mathfrak{A}\to\mathbb{C}$ a…

In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…

The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…

We derive the necessary and sufficient condition, for a given Polynomial Recurrence Sequence to converge to a given target rational K. By converge, we mean that the Nth term of the sequence, is equal to K, as N tends to positive infinity.…

For $\chi^2-$tests with increasing number of cells, Cramer-von Mises tests, tests generated $\mathbb{L}_2$- norms of kernel estimators and tests generated quadratic forms of estimators of Fourier coefficients, we find necessary and…

We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the…

We repurpose tools from the theory of quantitative rectifiability to study the qualitative rectifiability of measures in $\Bbb{R}^n$, $n\geq 2$. To each locally finite Borel measure $\mu$, we associate a function $\widetilde J_2(\mu, x)$…

If $X$ is an analytic metric space satisfying a very mild doubling condition, then for any finite Borel measure $\mu$ on $X$ there is a set $N\subseteq X$ such that $\mu(N)>0$, an ultrametric space $Z$ and a Lipschitz bijection $\phi:N\to…

We investigate a linear diffusion equation incorporating historical effects, characterised by a finite non-negative Borel measure on \((0, \mathfrak T]\). This approach accommodates both distributed memory and discrete delays within a…

Defining a condenser in a locally compact space as a locally finite, countable collection of Borel sets $A_i$, $i\in I$, with the sign $s_i=\pm1$ prescribed such that $A_i\cap A_j=\varnothing$ whenever $s_is_j=-1$, we consider a minimum…

A permutation sequence is said to be convergent if the density of occurrences of every fixed permutation in the elements of the sequence converges. We prove that such a convergent sequence has a natural limit object, namely a Lebesgue…

Let $K$ be a homogeneous self-similar set satisfying the strong separation condition. This paper is concerned with the quantitative recurrence properties of the natural map $T: K\rightarrow K$ induced by the shift. Let $\mu$ be the natural…

We employ positivity of Riesz functionals to establish representing measures (or approximate representing measures) for truncated multivariate moment sequences. For a truncated moment sequence $y$, we show that $y$ lies in the closure of…

We are interested in the problem of characterizing the correlations that arise when performing local measurements on separate quantum systems. In a previous work [Phys. Rev. Lett. 98, 010401 (2007)], we introduced an infinite hierarchy of…

It is assumed that in a measurement the system under study interacts with a macroscopic measuring apparatus, in such a way that the density matrix of the measured system evolves according to the Lindblad equation. Under an assumption of…

In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can,…

Let $B$ be an $n\times n$ real expanding matrix and $\mathcal{D}$ be a finite subset of $\mathbb{R}^n$ with $0\in\mathcal{D}$. The self-affine set $K=K(B,\mathcal{D})$ is the unique compact set satisfying the set-valued equation…

The paper deals with various centering problems for probability measures on finite dimensional vector spaces. We show that for every such measure there exists a vector $h$ satisfying $\mu*\delta(h)=S(\mu*\delta (h))$ for each symmetry $S$…

Let X be a strictly pseudoconcave domain in a closed polarized complex manifold (Y,L) where L is a (semi-)positive line bundle over Y. Any given Hermitian metric on L, together with a volume form, induces by restriction to X a Hilbert space…

For any bounded convex domain \Omega in R^N, we assign a positive finite Borel measure associated with the solution to a su-blinear elliptic equation in \Omega. We prove that this measure is weakly continuous in the sense of measure with…