Related papers: Determinantal approach to multiple orthogonal poly…
Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained…
The strict relation between some class of multiboson hamiltonian systems and the corresponding class of orthogonal polynomials is established. The correspondence is used effectively to integrate the systems. As an explicit example we…
As argued by Hone in the paper [Commun. Pure Appl. Math., 74(11):2310--2347, 2021], a ``mismatch" problem remained unsolved while he was investigating continued fraction expansions and Hankel determinants from hyperelliptic curves. In this…
In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second--order linear partial differential equations, which are admissible potentially…
We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal…
We identify the Atkin polynomials in terms of associated Jacobi polynomials. Our identificationthen takes advantage of the theory of orthogonal polynomials and their asymptotics to establish many new properties of the Atkin polynomials.…
The study of homological invariants such as Tor, Ext and local cohomology modules constitutes an important direction in commutative algebra. Explicit descriptions of these invariants are notoriously difficult to find and often involve…
We consider biorthogonal polynomials that arise in the study of a generalization of two--matrix Hermitian models with two polynomial potentials V_1(x), V_2(y) of any degree, with arbitrary complex coefficients. Finite consecutive…
The theory of polynomials orthogonal with respect to one inner product is classical. We discuss the extension of this theory to multiple inner products. Examples include the Lam\'e and Heine-Stieltjes polynomials.
We introduce seven families of stochastic systems of interacting particles in one-dimension corresponding to the seven families of irreducible reduced affine root systems. We prove that they are determinantal in the sense that all…
This paper is devoted to the study of general (Laurent) polynomial modifications of moment functionals on the unit circle, i.e., associated with hermitian Toeplitz matrices. We present a new approach which allows us to study polynomial…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
We derive formulas for characterizing bounded orthogonally additive polynomials in two ways. Firstly, we prove that certain formulas for orthogonally additive polynomials derived in \cite{Kusa} actually characterize them. Secondly, by…
Orthogonal polynomials in two variables on cubic curves are considered, including the case of elliptic curves. For an integral with respect to an appropriate weight function defined on a cubic curve, an explicit basis of orthogonal…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
A connection between matrix orthogonal polynomials and non-abelian integrable lattices is investigated in this paper. The normalization factors of matrix orthogonal polynomials expressed by quasi-determinant are shown to be solutions of…
We investigate several families of multiple orthogonal polynomials associated with weights for which the moment generating functions are hypergeometric series with slightly varying parameters. The weights are supported on the unit interval,…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of $n$ linear…
Given a parametrised weight function $\omega(x,\mu)$ such that the quotients of its consecutive moments are M\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \cite{IN2}. In the present paper…