Related papers: Fock representations of multicomponent (particular…

The $U^2$ norm gives a useful measure of quasirandomness for real- or complex-valued functions defined on finite (or, more generally, locally compact) groups. A simple Fourier-analytic argument yields an inverse theorem, which shows that a…

We construct symmetry generators and operators for $J\bar{T}$-deformed conformal field theories by generalizing the framework established for $T\bar{T}$ deformations. Working in the Hamiltonian formalism on the plane, we derive the symmetry…

In resonance to a recent geometric framework proposed by Douglas and Yang, a functional model for certain linear bounded operators with rank-one self-commutator acting on a Hilbert space is developed. By taking advantage of the refined…

We introduce and describe in second quantization a family of particle species with \(p=2,3,\dots\) exclusion and \(\theta=2\pi/p\) exchange statistics. We call these anyons Fock parafermions, because they are the particles naturally…

The Fock-like representations of the Relative Parabose Set (\textsc{Rpbs}) algebra in a single parabosonic and a single parafermionic degree of freedom are investigated. It is shown that there is an infinite family (parametrized by the…

We identify, through a change of variables, solution operators for evolution equations with generators given by certain simple first-order differential operators acting on Fock spaces. This analysis applies, through unitary equivalence, to…

We present an uniform construction of the solution to the Yang- Baxter equation with the symmetry algebra $s\ell(2)$ and its deformations: the q-deformation and the elliptic deformation or Sklyanin algebra. The R-operator acting in the…

The goal of the present paper is to push Sz.-Nagy--Foias model theory for a completely nonunitary Hilbert-space contraction operator $T$, to the case of a commuting pair of contraction operators $(T_1, T_2)$ having product $T = T_1 T_2$…

A proof is given for the Fourier transform for functions in a quantum mechanical Hilbert space on a non-compact manifold in general relativity. In the (configuration space) Newton-Wigner representation we discuss the spectral decomposition…

Recently A. Zamolodchikov obtained a series of identities for the expectation values of the composite operator T\bar{T} constructed from the components of the energy-momentum tensor in two-dimensional quantum field theory. We show that if…

Let $\nu$ be a finite measure on $\mathbb R$ whose Laplace transform is analytic in a neighborhood of zero. An anyon L\'evy white noise on $(\mathbb R^d,dx)$ is a certain family of noncommuting operators $\langle\omega,\varphi\rangle$ in…

We introduce an algebra $\mathcal W_t$ of linear operators that act continuously on each of the Fock spaces $F_t^p$, $1 \leq p \leq \infty$, and contains all Toeplitz operators with bounded symbols. We show that compactness, the spectrum,…

We consider various classes of bounded operators on the Fock space $F^2$ of Gaussian square integrable entire functions over the complex plane. These include Toeplitz (type) operators, weighted composition operators, singular integral…

The paper proposes a construction of a quantum differentiation operator defined on the spaces of complex-valued functions of $p$-adic argument, and taking values in the algebra of bounded operators on a Hilbert space. The properties of this…

We obtain criteria for the boundedness and compactness of weighted composition operators between different Fock spaces in $\mathbb{C}^n$. We also give estimates for essential norm of these operators.

Every unital nonselfadjoint operator algebra possesses canonical and functorial classes of faithful (even completely isometric) Hilbert space representations satisfying a double commutant theorem generalizing von Neumann's classical result.…

This work outlines a consistent method of identifying subsystems in finite-dimensional Hilbert spaces, independent of the underlying inner-product structure. Such Hilbert spaces arise in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics,…

The representation theory of deformed oscillator algebras, defined in terms of an arbitrary function of the number operator~$N$, is developed in terms of the eigenvalues of a Casimir operator~$C$. It is shown that according to the nature of…

This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with…

A model operator $H$ associated with the energy operator of a system describing three particles in interaction, without conservation of the number of particles, is considered. The precise location and structure of the essential spectrum of…