Related papers: Complex exceptional orthogonal polynomials and qua…
We give a Riemann-Hilbert approach to the theory of matrix orthogonal polynomials. We will focus on the algebraic aspects of the problem, obtaining difference and differential relations satisfied by the corresponding orthogonal polynomials.…
Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant role in several applications such as Hermite-Pad\'e…
Multiple Hermite polynomials are an extension of the classical Hermite polynomials for which orthogonality conditions are imposed with respect to $r>1$ normal (Gaussian) weights $w_j(x)=e^{-x^2+c_jx}$ with different means $c_j/2$, $1 \leq j…
The standard block orthogonal (SBO) polynomials $P_{i;n}(x), 0\le i\le n$ are real polynomials of degree $n$ which are orthogonal with respect to a first Euclidean scalar product to polynomials of degree less than $i$. In addition, they are…
Generalizations of the Hermite polynomials to many variables and/or to the complex domain have been located in mathematical and physical literature for some decades. Polynomials traditionally called complex Hermite ones are mostly…
We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that…
Integer partitions express the different ways that a positive integer may be written as a sum of positive integers. Here we explore the analytic properties of a new polynomial $f_\lambda(x)$ that we call the partition polynomial for the…
Classical orthogonal polynomial systems of Jacobi, Hermite and Laguerre have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a famous theorem by Bochner they…
For any orthogonal polynomials system on real line we construct an appropriate oscillator algebra such that the polynomials make up the eigenfunctions system of the oscillator hamiltonian. The general scheme is divided into two types: a…
Given a probability measure $\mu$ with infinite support on the unit circle $\partial\mathbb{D}=\{z:|z|=1\}$, we consider a sequence of paraorthogonal polynomials $\h_n(z,\lambda)$ vanishing at $z=\lambda$ where $\lambda \in \T$ is fixed. We…
Recently there has been a renewed interest in an extension of the notion of orthogonal polynomials known as multiple orthogonal polynomials. This notion comes from simultaneous rational approximation (Hermite-Pade approximation) of a system…
In this paper we present a generalization of the classical Hermite polynomials to the framework of Clifford-Dunkl operators. Several basic properties, such as orthogonality relations, recurrence formulae and associated differential…
We study Hermitian random matrix models with an external source matrix which has equispaced eigenvalues, and with an external field such that the limiting mean density of eigenvalues is supported on a single interval as the dimension tends…
A class of generalized complex polynomials of Hermite type, suggested by a special magnetic Schrodinger operator, is introduced and some related basic properties are discussed.
We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the…
This paper complements the recent investigation of \cite{DM} on the asymptotic behavior of polynomials orthogonal over the interior of an analytic Jordan curve $L$. We study the specific case of $L=\{z= w-1 +(w-1)^{-1},\ |w|=R\}$, for some…
We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical orthogonal polynomials. As an example we consider special…
For a certain class of partitions, a simple qualitative relation is observed between the shape of the Young diagram and the pattern of zeroes of the Wronskian of the corresponding Hermite polynomials. In the case of two-term Wronskian…
The aim of this paper is to bring into the picture a new phenomenon in the theory of orthogonal matrix polynomials satisfying second order differential equations. The last few years have witnessed some examples of a (fixed) family of…
Using Casorati determinants of Meixner polynomials $(m_n^{a,c})_n$, we construct for each pair $\F=(F_1,F_2)$ of finite sets of positive integers a sequence of polynomials $m_n^{a,c;\F}$, $n\in \sigma_\F$, which are eigenfunctions of a…