相关论文: On the connection between the Hilger and Radon--Ni…

052<p type="texpara" tag="Body Text" et="abstract" >A completely $n$ -positive linear map from a locally $C^{\ast}$-algebra $A$ to another locally $C^{\ast}$-algebra $B $is an $n\times n$ matrix whose elements are continuous linear maps…

Given positive integers $\ell<n$ and a real $d\in (\ell,n)$, we construct sets $K\subset \mathbb R^n$ with positive and finite Hausdorff $d-$measure such that the Radon-Nikodym derivative associated to all projections on $\ell-$dimensional…

Some topics concerning the Gould integral are presented here: new results of integrability on finite measure spaces with values in an M-space are given, together with a Radon-Nikodym theorem relative to a Gould-type integral of real…

The present paper is focused on the problem of recovering the Radon-Nikodym derivative under the big data assumption. To address the above problem, we design an algorithm that is a combination of the Nystr\"om subsampling and the standard…

We prove a dichotomy between absolute continuity and singularity of the Ginibre point process $\mathsf{G}$ and its reduced Palm measures $\{\mathsf{G}_{\mathbf{x}}, \mathbf{x} \in \mathbb{C}^{\ell}, \ell = 0,1,2\dots\}$, namely, reduced…

The paper contains a simple proof of the classical Hahn decomposition theorem for charges and, as a corollary, an explicit measurable in parameter construction of a Radon-Nikodym derivative of one measure by another.

In this article, the structure of semiclassical measures for solutions to the linear Schr\"{o}dinger equation on the torus is analysed. We show that the disintegration of such a measure on every invariant lagrangian torus is absolutely…

We prove a version of the Euler-Lagrange equations for certain problems of the calculus of variations on time scales with higher-order delta derivatives.

We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the…

In this paper we will give a categorical proof of the Radon-Nikodym theorem. We will do this by describing the trivial version of the result on finite probability spaces as a natural isomorphism. We then proceed to Kan extend this…

Given positive measures $\nu,\mu$ on an arbitrary measurable space $(\Omega, \mathcal F)$, we construct a sequence of finite partitions $(\pi_n)_n$ of $(\Omega, \mathcal F)$ s.t. $$ \sum_{A\in \pi_n: \mu(A)>0} 1_{A} \frac{\nu(A)}{\mu(A)}…

We let U=SU(2) and K=SO(2) and denote N_{U}(K) the normalizer of K in U. For a an element of U\ N_{U} (K), we let \mu_{a} be the normalized singular measure supported in KaK. For p a positive integer, it was proved that \mu_{a}^{( p)}, the…

In this paper, we introduce the concept of completely positive matrix of linear maps on Hilbert $A$-modules over locally $C^{*}$-algebras and prove an analogue of Stinespring theorem for it. We show that any two minimal Stinespring…

In this paper we present a generalization of the Radon-Nikodym theorem proved by Pedersen and Takesaki. Given a normal, semifinite and faithful (n.s.f.) weight $\phi$ on a von Neumann algebra M and a strictly positive operator $\delta$,…

We systematically study relative and absolute ${\Delta}_{\mathrm{dR}}^+$-crystals on the (log-) prismatic site of a smooth (resp.~ semi-stable) formal scheme. Using explicit computation of stratifications, we classify (local) relative…

The paper is concerned with one-dimensional two-sided Ornstein-Uhlenbeck type processes with delay or anticipation. We prove existence and uniqueness requiring almost sure boundedness on the left half-axis in case of delay and almost sure…

We prove new Hardy-type $\alpha$-conformable dynamic inequalities on time scales. Our results are proved by using Keller's chain rule, the integration by parts formula, and the dynamic H\"{o}lder inequality on time scales. When $\alpha=1$,…

We give a new characterization for mutual absolute continuity of probability measures on a filtered space. For this, we introduce a martingale limit $M$ that measures the similarity between the tails of the probability measures restricted…

The paper is devoted to the description a measurable time-interval (``proper time'') in the Hamiltonian version of general relativity with the Dirac-ADM metric. To separate the dynamical parameter of evolution from the space metric we use…

In this paper we prove well posedness for a system coupling a nonlinear Dirac with a Klein-Gordon equation that represents a toy model for the Helium atom with relativistic corrections: the wave function of the electrons interacts with an…