Related papers: Transfer operators and Hankel transforms: horosphe…
A quantum mechanical generalization of superstatistics is presented here based on the positive operator valued measure transformation property of the system density matrix. This procedure reveals that the origin of the fluctuating factors…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
We consider self-similar measures on $\mathbb R.$ The Hutchinson operator $H$ acts on measures and is the dual of the transfer operator $T$ which acts on continuous functions. We determine polynomial eigenfunctions of $T .$ As a…
We discuss the role of commuting operators for quantum superintegrable systems, showing how they are used to build eigenfunctions. These ideas are illustrated in the context of resonant harmonic oscillators, the Krall-Sheffer operators,…
In this paper, we consider the problem of quantization of classical St\"ackel systems and the problem of separability of related quantum Hamiltonians. First, using the concept of St\"ackel transform, all considered systems are expressed by…
This paper introduces the class of grey-scale image stack operators as those that (a) map binary-images into binary-images and (b) commute on average with cross-sectioning. Equivalently, stack operators are 1-Lipchitz extensions of set…
The purpose of this paper is to present an algorithm for evaluating Hankel transform of the null and the first kind. The result is the exact analytical representation as the series of the Bessel and Struve functions multiplied by the…
Linear transfers between probability distributions were introduced in [5,6] in order to extend the theory of optimal mass transportation while preserving the important duality established by Kantorovich. It is shown here that $\{0,…
This paper seeks to extend the theory of composition operators on analytic functional Hilbert spaces from analytic symbols to quasiconformal ones. The focus is the boundedness but operator-theoretic questions are discussed as well. In…
We introduce and study the class of linear transfers between probability distributions and the dual class of Kantorovich operators between function spaces. Linear transfers can be seen as an extension of convex lower semi-continuous…
In this paper we perform an explicit diagonalization of Hankel integral operators $ K^{(0)}, K^{(1)}, K^{(2)}, ... $ It turns out that each of these operators has a simple purely absolutely continuous spectrum filling in the interval $…
We give criteria for the membership of Hankel operators on the Hardy space on the disc in the Dixmier class, and establish estimates for their Dixmier trace. In contrast to the situation in the Bergman space setting, it turns out that there…
The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring of translational operators in the spectral parameter. In the rational limit, these…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
We introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear input-plant-output systems to arbitrary quantum nonlinear Markovian input-output models. This is intended as a tool in the…
We study homotopy-coherent commutative multiplicative structures on equivariant spaces and spectra. We define N-infinity operads, equivariant generalizations of E-infinity operads. Algebras in equivariant spectra over an N-infinity operad…
Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter $k\in(0,1)$ are presented. The Hankel matrices are regarded as matrix operators on the Hilbert space $\ell^{2}(\mathbb{N}_{0})$ and the solution of the…
Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…
We employ the framework of operational calculus to derive the operators associated with the spherical mean and a class of related averaging means of a function in $n$-dimensional space. Beginning with the classical definition of the…
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of…