Related papers: The Analytic Theory of Matrix Orthogonal Polynomia…

We establish an analogue of the fundamental theorem of algebra for polynomial matrix equations, in which the matrices-coefficients and unknown matrix are assumed to be circulant matrices.

We survey some recent developments in the analytic theory of multiple Dirichlet series with arithmetical coefficients on the numerators.

We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via…

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…

We introduce the concept of reflexive moment functional in two variables and the definition of reflexive orthogonal polynomial system. Also reverse matrices and their interesting algebraic properties are studied. Reverse matrices and…

This paper surveys a comprehensive, although not exhaustive, sampling of graph polynomials with the goal of providing a brief overview of a variety of techniques defining a graph polynomial and then for decoding the combinatorial…

We describe the images of multilinear polynomials of degree up to four on the upper triangular matrix algebra.

In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…

We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.

A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.

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…

Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we…

Matrix-valued Cauchy bi-orthogonal polynomials were proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in four-term recurrence relation for matrix-valued Cauchy bi-orthogonal polynomials…

We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a $p$-adic field, together with relevant arithmetic information about the fields generated by the irreducible…

We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split…

In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also…

A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a…

An observation on Hall-Littlewood polynomials.

This work is divided into three parts. The first part concerns polynomials in one variable with all real roots. We consider linear transformations that preserve real rootedness, as well as matrices that preserve interlacing. The second part…

We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and…