Related papers: On Operator-valued Semicircular Random Variables
For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…
The article is devoted to stochastic processes with values in finite-dimensional vector spaces over infinite locally compact fields with non-trivial non-archimedean valuations. Infinitely divisible distributions are investigated. Theorems…
Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are…
The interpretation of quantum mechanics due to Lande' is applied to the connection between wave mechanics and matrix mechanics. The connection between the differential eigenvalue equation and the matrix eigenvalue equation for an operator…
We demonstrate quantum algorithms to implement pseudo-random operators that closely reproduce statistical properties of random matrices from the three universal classes: unitary, symmetric, and symplectic. Modified versions of the…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
We propose an operational quasiprobability function for qudits, enabling a comparison between quantum and hidden-variable theories. We show that the quasiprobability function becomes positive semidefinite if consecutive measurement results…
The space of positive operator-valued measures on the Borel sets of a compact (or even locally compact) Hausdorff space with values in the algebra of linear operators acting on a d-dimensional Hilbert space is studied from the perspectives…
We study the characteristic function and moments of the integer-valued random variable $\lfloor X+\alpha\rfloor$, where $X$ is a continuous random variables. The results can be regarded as exact versions of Sheppard's correction. Rounded…
In this article we consider means of positive bounded linear operators on a Hilbert space. We present a complete theory that provides a framework which extends the theory of the Karcher mean, its approximating matrix power means, and a…
We give a local characterization of the class of functions having positive distributional derivative with respect to $\bar{z}$ that are almost everywhere equal to one of finitely many analytic functions and satisfy some mild non-degeneracy…
We develop a systematic theory of eventually positive semigroups of linear operators mainly on spaces of continuous functions. By eventually positive we mean that for every positive initial condition the solution to the corresponding Cauchy…
In this article we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master…
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth.This fact motivates the consideration of subdifferentials for such typically just continuous…
We give a survey of some results, mainly obtained by the authors and their collaborators, on spectral properties of the magnetic Schr\"odinger operators in the semiclassical limit. We focus our discussion on asymptotic behavior of the…
We consider solutions of the Cauchy problem for semilinear equations with (possibly) different L\'evy operators. We provide various results on their convergence under the assumption that symbols of the involved operators converge to the…
The divergence-like operator on an odd symplectic superspace which acts invariantly on a specially chosen odd vector field is considered. This operator is used to construct an odd invariant semidensity in a geometrically clear way. The…
In this paper, we consider pseudodifferential operators on the torus with operator-valued symbols and prove continuity properties on vector-valued toroidal Besov spaces, without assumptions on the underlying Banach spaces. The symbols are…
In this paper we obtain the weak type (1,1) boundedness of Calderon-Zygmund operators acting over operator-valued functions. Our main tools for its solution are a noncommutative form of Calderon-Zygmund decomposition in conjunction with a…