Related papers: On the Multiplicity of Density Operator Representa…
This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory.…
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…
We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space…
Density matrices are powerful mathematical tools for the description of closed and open quantum systems. Recently, methods for the direct computation of density matrix elements in scalar quantum field theory were developed based on thermo…
A parametrization of multipartite separable states in a finite-dimensional Hilbert space is suggested. It is proved to be a diffeomorphism between the set of zero-trace operators and the interior of the set of separable density operators.…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
Let $\Delta$ be a linear differential operator acting on the space of densities of a given weight $\lo$ on a manifold $M$. One can consider a pencil of operators $\hPi(\Delta)=\{\Delta_\l\}$ passing through the operator $\Delta$ such that…
Dynamical sampling deals with representations of a frame $\{ f_k \}_{k=1}^\infty$ as an orbit $\{ T^n \varphi \}_{n=0}^\infty$ of a linear and possibly bounded operator $T$ acting on the underlying Hilbert space. It is known that the desire…
Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a…
We gave a simple derivation of density operator with the quantum analysis. We dealt with the functional of a density operator, and applied maximum entropy principle. We obtained easily the density operators for the Tsallis entropy and…
In this work, the density in $H(b)$ spaces of finitely connected planar domains and the boundedness of composition operators on these function spaces are studied. Density of the algebra $\mathcal{A}(D)$ is considered for both in the cases…
A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…
In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it's dual space. The Factorization Method uses Picard's Criteria to define an indicator function to…
It is shown that an operator can be defined in the abstract space of random matrices ensembles whose matrix elements statistical distribution simulates the behavior of the distribution found in real physical systems. It is found that the…
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…
A function which is analytic and bounded in the Unit disk is called a generator for the Hardy space or the Bergman space if polynomials in that function are dense in the corresponding space. We characterize generators in terms of sub-spaces…
A dual frames multiplier is an operator consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames in a Hilbert space, respectively. In this paper we investigate the…
In this paper, we describe the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…
Quantum Iterated Function System on a complex projective space is defined by a family of linear operators on a complex Hilbert space. The operators define both the maps and their probabilities by one algebraic formula. Examples with…
Classical density functional theory (cDFT) provides a systematic approach to predict the structure and thermodynamic properties of chemical systems through the single-molecule density profiles. Whereas the statistical-mechanical framework…