相关论文: Generators of Dynamical Systems on Hilbert Modules

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…

A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space $\mathcal{H}$ is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group $G$ on…

In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…

We explicitly construct generators of the rational homotopy groups of the space of stable h-cobordisms of the classifying space of a cyclic group of order n by generalizing a construction of Hatcher. This result will be used in a separate…

For a general discrete dynamics on a Banach and Hilbert spaces we give a necessary and sufficient conditions of the existence of bounded solutions under assumption that the homogeneous difference equation admits an exponential dichotomy on…

Generators and defining relations for wreath products of groups are given. Under some condition (conormality of the generators) they are minimal. In particular, it is just the case for the Sylow subgroups of the symmetric groups.

We provide a general framework for the realization of powers or functions of suitable operators on Dirichlet spaces. The first contribution is to unify the available results dealing with specific geometries; a second one is to provide new…

A refined notion of curvature for a linear system of Hermitian vector spaces, in the sense of Grothendieck, leads to the unitary classification of a large class of analytic Hilbert modules. Specifically, we study Hilbert sub-modules, for…

We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then…

We propose a high dimensional generalisation of the standard Klein bottle, going beyond those considered previously. We address the problem of generating continuous scalar fields (distributions) and dynamical systems (flows) on such state…

We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We…

Symmetries of finite Heisenberg groups represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. This short contribution presents extension of previous investigations to composite quantum systems…

A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…

Some consequences of promoting the object of noncommutativity ${\mathbf \theta}^{ij}$ to an operator in Hilbert space are explored. Consequently, a consistent algebra involving the enlarged set of canonical operators is obtained, which…

We study, to certain Banach spaces $X$, families of weighted composition operators. Notably, we show that if this family form a strongly continuous semigroup, then its infinitesimal generator ($\Gamma, D(\Gamma)$) is given by $\Gamma f =…

Little is known about the generators system of the higher dimensional Picard modular groups. In this paper, we prove that the higher dimensional Eisenstein--Picard modular group $\mathbf{PU}(3,1;\mathbb{Z}[\omega_3])$ in three complex…

For a tropical curve and a finite subgroup of the isometry group of the tropical curve, we prove, extending the work by Haase, Musiker and Yu, that the invariant part of the complete linear system associated to a invariant effective divisor…

Most generalized fractional operators rely on prescribed memory kernels, restricting hereditary behavior to predefined forms and limiting flexibility in modeling diverse memory effects. Motivated by these limitations, this paper develops a…

We characterize weak* closed unital vector spaces of operators on a Hilbert space $H$. More precisely, we first show that an operator system, which is the dual of an operator space, can be represented completely isometrically and weak*…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…