Related papers: On Operator-valued Semicircular Random Variables
Given a positive operator-valued measure $\nu$ acting on the Borel sets of a locally compact Hausdorff space $X$, with outcomes in the algebra $\mathcal B(\mathcal H)$ of all bounded operators on a (possibly infinite-dimensional) Hilbert…
Multivariate random fields whose distributions are invariant under operator-scalings in both time-domain and state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are…
In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued…
The paper deals with the semi-Dirac operator in a half-space arising in the description of quasiparticles in quantum mechanics as well as in semi-metals materials and related structures. It completely shows the self-adjointness, computes…
We review recent probabilistic results on covariant Schr\"odinger operators on vector bundles over (possibly locally infinite) weighted graphs, and explain applications like semiclassical limits. We also clarify the relationship between…
We investigate fractional moments and expectations of power means of complex-valued random variables by using fractional calculus. We deal with both negative and positive orders of the fractional derivatives. The one-dimensional…
We give two new simple characterizations of the Cauchy distribution by using the M\"obius and Mellin transforms. They also yield characterizations of the circular Cauchy distribution and the mixture Cauchy model.
An atomic random complex measure defined on the unit disk with Normally distributed moments is considered. An approximation to the distribution of the zeros of its Cauchy transform is computed. Implications of this result for solving…
In this paper we characterize multiplication operators induced by operator valued maps on Banach function spaces. We also study multiplication semigroups and stability of these operators.
Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and…
This paper considers strongly continuous semigroups of operators on Banach lattices which are locally eventually positive, a property that was first investigated in the context of concrete fourth-order evolution equations. We construct a…
We set-up and solve the Cauchy problem for Schr\"odinger-type differential operators with generalized functions as coefficients, in particular, allowing for distributional coefficients in the principal part. Equations involving such kind of…
We consider a class of one-dimensional nonselfadjoint semiclassical pseudo-differential operators, subject to small random perturbations, and study the statistical properties of their (discrete) spectra, in the semiclassical limit $h\to 0$.…
In this work we continue the study of the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint (pseudo)differential operators with small random perturbations, by treating the case of multiplicative perturbations in…
We study the Cauchy problem for the first order evolutive Hamilton-Jacobi equation with a Lipschitz initial condition. The Hamiltonian is not necessarily convex in the momentum variable and not a priori compactly supported. We build and…
We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced by Kossakowski in…
The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential…
We study the angular process related to random walks in the Euclidean and in the non-Euclidean space where steps are Cauchy distributed. This leads to different types of non-linear transformations of Cauchy random variables which preserve…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…
The purpose of this paper is to investigate the stationary dense operators and their connection to distribution semigroups and abstract Cauchy problem in sequentially complete spaces.