Related papers: Higher order self-adjoint operators with polynomia…
We introduce the concept of $\D$-operators associated to a sequence of polynomials $(p_n)_n$ and an algebra $\A$ of operators acting in the linear space of polynomials. In this paper, we show that this concept is a powerful tool to generate…
Given a pair of smooth transversally intersecting manifolds in some ambient manifold, we construct an operator algebra generated by pseudodifferential operators and the (co)boundary operators associated with the submanifolds. We show that…
In this paper, we investigate the spectrum of the self adjoint differential operator with operator coefficitent in a separable Hilbert space. We also derive asymptotic formulas for the sum of eigenvalues of this operator.
We study selfadjoint functors acting on categories of finite dimensional modules over finite dimensional algebras with an emphasis on functors satisfying some polynomial relations. Selfadjoint functors satisfying several easy relations, in…
Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality.…
Starting from Rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variable on uniform lattice. In order to have these operators mutually adjoint we…
In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.
This paper gives a classification of first order polynomial differential operators of form $\mathscr{X} = X_1(x_1,x_2)\delta_1 + X_2(x_1,x_2)\delta_2$, $(\delta_i = \partial/\partial x_i)$. The classification is given through the order of…
We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and $q$-difference equations for these polynomials. A general functional equation is found which allows one to relate…
A special class of generalized Jacobi operators which are self-adjoint in Krein spaces is presented. A description of the resolvent set of such operators in terms of solutions of the corresponding recurrence relations is given. In…
We consider the self-adjoint fourth-order operator with real $1$-periodic coefficients on the unit interval. The spectrum of this operator is discrete. We determine the high energy asymptotics for its eigenvalues.
A criterion and sufficient conditions for a vector to be a cyclic vector for a class of self-adjoint operators are obtained.
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…
A generic differential operator on the vectorial space of polynomial functions was presented in a recent work and applied in the study of differential relations fulfilled by polynomial sequences either orthogonal or 2-orthogonal. Using the…
This paper argues that non-self-adjoint operators can be observables. There are only four ways for this to occur: non-self-adjoint observables can either be normal operators, or be symmetric, or have a real spectrum, or have none of these…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
We discuss self-adjoint operators given formally by expressions quadratic in bosonic creation and annihilation operators. We give conditions when they can be defined as self-adjoint operators, possibly after an infinite renormalization. We…
We study polynomial functors in the incompressible category $\text{Ver}_4^+$, which can be viewed as super polynomial functors in characteristic 2. Concretely, we classify additive, exact and simple polynomial functors, and describe how…
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,…
This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.