相关论文: Monic non-commutative orthogonal polynomials

We establish the asymptotic zero distribution for polynomials generated by a four-term recurrence relation with varying recurrence coefficients having a particular limiting behavior. The proof is based on ratio asymptotics for these…

In this paper we consider several problems of joint similarity to tuples of bounded linear operators in noncommutative polydomains and varieties associated with sets of noncommutative polynomials. We obtain analogues of classical results…

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…

For a system of two measures supported on a starlike set in the complex plane, we study asymptotic properties of associated multiple orthogonal polynomials $Q_{n}$ and their recurrence coefficients. These measures are assumed to form a…

In this study, we present a novel family of Meixner-type $d$-orthogonal polynomials, which are distinguished as a particular subset of multiple orthogonal polynomials. We demonstrate their connection to the Lie algebra $\mathfrak{su}(1,1)$…

We prove two "master" convolution theorems for multivariate determinantal polynomials. The methods used include basic properties of what we call a "minor-orthogonal" ensemble as well as properties of the mixed discriminant of matrices. We…

A general theorem due to Howe of dual action of a classical group and a certain non-associative algebra on a space of symmetric or alternating tensors is reformulated in a setting of second quantization, and familiar examples in atomic and…

We give new definitions for the determinant over commutative ring $K$, noncommutative ring $\mathbf{K}$, noncommutative ring $\mathcal{K}$ with associative powers, over noncommutative nonassociative ring $\mathfrak{K}$, and study their…

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 show that any differential operator of the form $L(y)=\sum_{k=0}^{k=N} a_{k}(x) y^{(k)}$, where $a_k$ is a real polynomial of degree $\leq k$, has all real eigenvalues in the space of polynomials of degree at most n, for all n. The…

In this paper we define the notion of monic representation for the $C^*$-algebras of finite higher-rank graphs with no sources, and undertake a comprehensive study of them. Monic representations are the representations that, when restricted…

We investigate polynomials, called m-polynomials, whose generator polynomial has coefficients that can be arranged as a matrix, where q is a positive integer greater than one. Orthogonality relations are established and coefficients are…

This paper studies a new family of Angelesco multiple orthogonal polynomials with shared orthogonality conditions with respect to a system of weight functions, which are complex analogues of Pascal distributions on a legged star-like set.…

We study a class of meromorphic modular forms characterised by Fourier coefficients that satisfy certain divisibility properties. We present new candidates for these so-called magnetic modular forms, and we conjecture properties that these…

While considering nonlinear coherent states with specific anti-holomorphic coefficients $\bar{z}^n/\sqrt{x_n!}$, we identify as first associated Meixner-Pollaczek polynomials the orthogonal polynomials arising from shift operators which are…

Using an algebraic method for solving the wave equation in quantum mechanics, we encountered a new class of orthogonal polynomials on the real line. It consists of a four-parameter polynomial with continuous spectrum on the whole real line…

We show how a certain limit of the nonsymmetric Macdonald polynomials appears in the representation theory of semisimple groups over p--adic fields as matrix coefficients for the unramified principal series representations. The result is…

There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…

Given a function $b$, holomorphic on the disc and bounded by 1, one can construct an associated reproducing kernel Hilbert space called the de Branges--Rovnyak space $H(b)$. We explore representations of such spaces via descriptions of the…

Considering commutator monomials of the non-commutative associative variables $X_1,\ldots,X_n$; we determine the maximal possible number of alternating associative monomials in their noncommutative polynomial expansions. This is achieved by…