Related papers: Subnormal operators regarded as generalized observ…
Let $T\in\mathbb{B}(\mathscr{H})$ and $T=U|T|$ be its polar decomposition. We proved that (i) if $T$ is log-hyponormal or $p$-hyponormal and $U^n=U^\ast$ for some $n$, then $T$ is normal; (ii) if the spectrum of $U$ is contained in some…
Classical sequential growth models for causal sets provide an important step towards the formulation of a quantum causal set dynamics. The covariant observables in a class of these models known as generalised percolation have been…
In this paper we extensively investigate the class of conditionally positive definite operators, namely operators generating conditionally positive definite sequences. This class itself contains subnormal operators, $2$- and $3$-isometries…
This paper outlines a covariant theory of operators defined on groups and homogeneous spaces. A systematic use of groups and their representations allows to obtain results of algebraic and analytical nature. The consideration is…
Supersymmetric quantum mechanics has many applications, and typically uses a raising and lowering operator formalism. For one dimensional problems, we show how such raising and lowering operators may be generalized to include an arbitrary…
Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…
While the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid…
Given an observable and its operator product expansion (OPE), we present expressions that carefully disentangle truncated sums of the perturbative series in powers of $\alpha$ from the non-perturbative (NP) corrections. This splitting is…
Normalization constant in the eigenstate appearing in the eigenvalue problem of the su(1,1)-algebra is discussed. This normalization constant is expressed in terms of the Gauss' hypergeometric series which is not absolutely convergent. It…
Definition of generalized normal form for a system of ODEs corresponding to an infinitesimal symplectic or contact transformation near a singular point, with an arbitrary polynomial unperturbed part, and a method of its finding are…
The concepts of superposition and of transition probability, familiar from pure states in quantum physics, are extended to locally normal states on funnels of type I$_\infty$ factors. Such funnels are used in the description of infinite…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
We give an overview and extension of recent results on ergodic random Schr\"odinger operators for models on $\mathbb{Z}^d$. The operators we consider are defined on combinatorial or metric graphs, with random potentials, random boundary…
In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm in the unit sphere. We prove important results concerning the characterization of the AN operators, see Definition 1.2. The class of AN…
Supersymmetry might be broken, in the real world, by anomalies that affect composite operators, while leaving the action supersymmetric. New constraint equations that govern the composite operators and their anomalies are examined. It is…
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…
An extension of the Semimicroscopic Algebraic Cluster Model (SACM) is proposed, based on the pseudo-SU(3) model. The Hamiltonian and the spectroscopic factor operator of the model are presented and a procedure of constructing the model…
A criterion for subnormality of unbounded composition operators in L2-spaces, written in terms of measurable families of probability measures satisfying the so-called consistency condition, is established. It becomes a new characterization…
An extension of the Super KdV integrable system in terms of operator valued functions is obtained. Following the ideas of Gardner, a general algebraic approach for finding the infinitely many conserved quantities of integrable systems is…
Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…