相关论文: QES systems, invariant spaces and polynomials recu…

Baskakov operators and their inverses can be expressed as linear differential operators on polynomials. Recurrence relations are given for the computation of these coefficients. They allow the construction of the associated Baskakov…

We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly…

Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…

The notion of the eigenvalue problem in the Fock space with polynomial eigenfunctions is introduced. This problem is classified by using the finite-dimensional representations of the $\mathfrak{sl}(2)$-algebra in Fock space. In the complex…

We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.

In this paper, we describe a class of elements in the ring of $\mathrm{SL}(V)$-invariant polynomial functions on the space of configurations of vectors and linear forms of a 3-dimensional vector space $V.$ These elements are related to one…

Let $T$ be a linear operator on an $\mathbb{F}_q$-vector space $V$ of dimension $n$. For any divisor $m$ of $n$, an $m$-dimensional subspace $W$ of $V$ is $T$-splitting if $$ V =W\oplus TW\oplus \cdots \oplus T^{d-1}W, $$ where $d=n/m$. Let…

Recently Sarah Bockting-Conrad introduced the double lowering operator $\psi$ for a tridiagonal pair. Motivated by $\psi$ we consider the following problem about polynomials. Let $\mathbb F$ denote an algebraically closed field. Let $x$…

For operators generated by a certain class of infinite band matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying higher order finite difference equations. This…

New examples of matrix quasi exactly solvable Schroedinger operators are constructed. One of them constitutes a matrix generalization of the quasi exactly solvable anharmonic oscillator, the corresponding invariant vector space is…

The Kalman variety of a linear subspace in a vector space consists of all endomorphism that possess an eigenvector in that subspace. We study the defining polynomials and basic geometric invariants of the Kalman variety.

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…

We study several classes of indecomposable representations of quivers on infinite-dimensional Hilbert spaces and their relation. Many examples are constructed using strongly irreducible operators. Some problems in operator theory are…

We introduce and study some special classes of ladder operators in finite-dimensional Hilbert spaces. In particular we consider a truncated version of quons, their {\em psudo-}version, and a third family of operators acting on a closed…

For a Lie algebra ${\mathcal L}$ with basis $\{x_1,x_2,\cdots,x_n\}$, its associated characteristic polynomial $Q_{{\mathcal L}}(z)$ is the determinant of the linear pencil $z_0I+z_1\text{ad} x_1+\cdots +z_n\text{ad} x_n.$ This paper shows…

Integral representations of two $q$-difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to $q$-difference equations in the complex domain. Both representations are unified through…

In this paper we present how spectral properties of certain linear operators vary when operators are considered in different Hilbert spaces having common dense domain as the space of polynomials in one real variable with complex…

We analyze the behavior of the iterates of composition operators defined by polynomials acting on global classes of ultradifferentiable functions of Beurling type and being invariant under Fourier transform. We characterize the polynomials…

We study the computational complexity of decomposing finite discrete dynamical systems (FDDSs) in terms of the semiring operations of alternative and synchronous execution, which is useful for the analysis of discrete phenomena in science…