Related papers: Higher order deformed elliptic Ruijsenaars operato…
A Heisenberg-Clifford realization of a deformed $U(sl_{2})$ by two parameters $p$ and $q$ is discussed. The commutation relations for this deformed algebra have interesting connection with the theta functions.
An example due to Pisier shows that two commuting, completely polynomially bounded Hilbert space operators may not be simultaneously similar to contractions. Thus, while each operator is individually similar to a contraction, the pair is…
We describe a set of conformally covariant boundary operators associated to the sixth-order GJMS operator on a conformally invariant class of manifolds which includes compactifications of Poincar\'e--Einstein manifolds. This yields a…
We construct all (2+1)-dimensional PDEs depending only on 2nd-order derivatives of unknown which have the Euler-Lagrange form and determine the corresponding Lagrangians. We convert these equations and their Lagrangians to two-component…
In this paper, we consider the boundedness of a class of sublinear operators and their commutators by with rough kernels associated with Calderon-Zygmund operator, Hard-Littlewood maximal operator, fractional integral operator, fractional…
We consider a class of multiparameter singular Radon integral operators on the Heisenberg group ${\mathbb H}^1$ where the underlying variety is the graph of a polynomial. A remarkable difference with the euclidean case, where Heisenberg…
We study the quantum analogs of tops on Lie algebras $so(4)$ and $e(3)$ represented by differential operators.
We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…
We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a…
Progress along the line of a previous article are reported. One main point is to include chiral operators with fractional quantum group spins (fourth or sixth of integers) which are needed to achieve modular invariance. We extend the study…
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…
In this paper we study rank two commuting ordinary differential operators with polynomial coefficients and the orbit space of the automorphisms group of the first Weyl algebra on such operators. We prove that for arbitrary fixed spectral…
We reconsider the (non-relativistic) quantum theory of indistinguishable particles on the basis of Rieffel's notion of C*-algebraic (`strict') deformation quantization. Using this formalism, we relate the operator approach of Messiah and…
The purpose of the present paper is to pursue further study of a class of linear bounded operators, known as n-quasi-m-isometric operators acting on an infinite complex separable Hilbert space H. This generalizes the class of m-isometric…
Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide applications in modern physics and connection to many domains in…
In the previous paper we introduced a commuting family of Baxter Q-operators for the quantum Ruijsenaars hyperbolic system. In the present work we show that the wave functions of the quantum system found by M. Halln\"as and S. Ruijsenaars…
We revise the construction of creation/annihilation operators in quantum mechanics based on the representation theory of the Heisenberg and symplectic groups. Besides the standard harmonic oscillator (the elliptic case) we similarly treat…
We describe integrable elliptic q-deformed anisotropic long-range spin chain. The derivation is based on our recent construction for commuting anisotropic elliptic spin Ruijsenaars-Macdonald operators. We prove that the Polychronakos…
We study boundary value problems for some differential operators on Euclidean space and the Heisenberg group which are invariant under the conformal group of a Euclidean subspace resp. Heisenberg subgroup. These operators are shown to be…
The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral…