Related papers: Wiener's Tauberian theorem in classical and quantu…

We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…

By relating notions from quantum harmonic analysis and band-dominated operator theory, we prove that over any locally compact abelian group $G$, the operator algebra $\mathcal C_1$ from quantum harmonic analysis agrees with the intersection…

We consider the classical Wiener-Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known…

We extend the well-known Katznelson-Tzafriri theorem, originally posed for power-bounded operators, to the case of Ces\`aro bounded operators of any order $\alpha>0.$ For this purpose, we use a functional calculus between a new class of…

Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This…

A new approach to problems of the Uncertainty Principle in Harmonic Analysis, based on the use of Toeplitz operators, has brought progress to some of the classical problems in the area. The goal of this paper is to develop and systematize…

The main goal of this note is to characterize the necessary and sufficient conditions for a composition operator to act between spaces of mappings of bounded Wiener variation in a normed-valued setting. The necessary and sufficient…

We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…

A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…

We give a survey of how the relatively young theory of operator spaces has led to a deeper understanding of the Fourier algebra of a locally compact group (and of related algebras).

Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the…

Weaver has recently defined the notion of a quantum relation on a von Neumann algebra. We demonstrate that the corresponding notion of a quantum function between two von Neumann algebras coincides with that of a normal unital…

The factorisation of scattering amplitude is described by the Weinberg theorem. In this talk, we will show the universality of the theorem at the next leading correction of the soft expansion. For that we will derive the soft operator by…

The aim of the present paper is to define compact operators on asymmetric normed spaces and to study some of their properties. The dual of a bounded linear operator is defined and a Schauder type theorem is proved within this framework. The…

The correspondence between classical and quantum invariants is established. The Ermakov Lewis quantum invariant of the time dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase…

With the use of tensor product of Hilbert space, and a diagonalization procedure from operator theory, we derive an approximation formula for a general class of stochastic integrals. Further we establish a generalized Fourier expansion for…

The mathematical description of the quantum harmonic oscillator is essentially based on the Gaussian function. In the case of a quantum oscillator with finite-dimensional Hilbert space, the position space consists in a finite number of…

We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…

In this paper, a new generalized Bernstein-Bezier type operators is constructed.The estimates of the moments of these operators are investigated. The rate of convergence in terms of modulus of continuity is given. Then, the equivalent…

The purpose of this paper is to study sparse domination estimates of composition operators in the setting of complex function theory. The method originates from proofs of the $A_2$ theorem for Calder\'on-Zygmund operators in harmonic…