Related papers: On the hermiticity of q-differential operators and…
We define a generalized $(q;\alpha,\beta,\gamma;\nu)$-deformed oscillator algebra and study the number of its characteristics. We describe the structure function of deformation, analyze the classification of irreducible representations and…
In the present paper, we study quantum Sobolev spaces whose elements are operators of the Hilbert-Schmidt class. We construct these Sobolev spaces from the Fourier transform for operators. Next, we obtain continuous embedding theorems.…
The trigonometric quantized Knizhnik-Zamolodchikov equation (qKZ equation) associated with the quantum group $U_q(sl_2)$ is a system of linear difference equations with values in a tensor product of $U_q(sl_2)$ Verma modules. We solve the…
We study, in a global uniform manner, the quotient of the ring of polynomials in l sets of n variables, by the ideal generated by diagonal quasi-invariant polynomials for general permutation groups W=G(r,n). We show that, for each such…
Parallels between the notions of nonlinear pseudobosons and of an apparent non-Hermiticity of observables as shown in paper I (arXiv: 1109.0605) are demonstrated to survive the transition to the quantum models based on the use of unbounded…
In this paper, we study and classify Hilbert space representations of cross product *-algebras of the quantized enveloping algebra $U_q(e_2)$ with the coordinate algebras $O(E_q(2))$ of the quantum motion group and $O(\C_q)$ of the complex…
We consider elliptic differential operators on either the entire Euclidean space $\mathbb{R}^d$ or on subsets consisting of a cube $\Lambda_L$ of integer length $L$. For eigenfunctions of the operator, and more general solutions of elliptic…
A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…
We define a one-parameter family of two-sided coideals in U_q(gl(n)) and study the corresponding algebras of infinitesimally right invariant functions on the quantum unitary group U_q(n). The Plancherel decomposition of these algebras with…
Let $p$ be an idempotent ultrafilter over $\mathbb{N}$. For a positive integer $N$, let ${\cal P}_{\leq N}$ denote the additive group of polynomials $P\in\mathbb{Z}[x]$ with ${\rm deg}\, P\leq N$ and $P(0)=0$. Given a unitary operator $U$…
This paper is the survey of some of our results related to $q$-deformations of the Fock spaces and related to $q$-convolutions for probability measures on the real line $\mathbb{R}$. The main idea is done by the combinatorics of moments of…
We consider coefficient bodies $\mathcal M_n$ for univalent functions. Based on the L\"owner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov's operators for a…
Let P be a parabolic subgroup of a simple affine algebraic group G defined over C and X a compact connected K\"ahler manifold. L. \'Alvarez-C\'onsul and O. Garc\'ia-Prada associated to these a quiver Q and representations of Q into…
Let $M^n$ be either a simply connected space form or a rank-one symmetric space of noncompact type. We consider Weingarten hypersurfaces of $M\times\mathbb R$, which are those whose principal curvatures $k_1,\dots ,k_n$ and angle function…
In this paper we compute the first and second variation of the normalized Einstein-Hilbert functional on CR manifolds. We characterize critical points as pseudo-Einstein structures. We then turn to the second variation on standard spheres.…
The classical Hilbert space formulation of the axioms of Quantum Mechanics appears to leave open the question whether the Hermitian operators which are associated with the observables of a finite non-relativistic quantum system are uniquely…
A non--commutative analogue of the classical differential forms is constructed on the phase--space of an arbitrary quantum system. The non--commutative forms are universal and are related to the quantum mechanical dynamics in the same way…
In this paper we discuss a formulation of relativistic quantum mechanics that uses Euclidean Green functions or generating functionals as input. This formalism has a close relation to quantum field theory, but as a theory of linear…
We obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric on a general weighted Hardy space of analytic functions in the unit disk whose reproducing kernel has the usual natural form. This turns…