Related papers: Two-dimensional diffusion orthogonal polynomials o…

A weighted bicolored plane tree is a bicolored plane tree whose edges are endowed with positive integral weights. The degree of a vertex is defined as the sum of the weights of the edges incident to this vertex. Using the theory of dessins…

We study the orthogonal projection of homogeneous polynomials onto the space of homogeneous polyharmonic polynomials. To do this we derive the decomposition of homogeneous polynomials in terms of the Kelvin transform of derivatives of the…

In this paper we present an algebraic study concerning the general second order linear differential equation with polynomial coefficients. By means of Kovacic's algorithm and asymptotic iteration method we find a degree independent…

We propose a general method to construct symmetric tensor polynomials in the D-dimensional Euclidean space which are orthonormal under a general weight. The D-dimensional Hermite polynomials are a particular case of the present ones for the…

We study algebraic structures ($L_\infty$ and $A_\infty$-algebras) introduced by Gaiotto, Moore and Witten in their recent work devoted to certain supersymmetric 2-dimensional massive field theories. We show that such structures can be…

In this paper, monic polynomials orthogonal with deformation of the Freud-type weight function are considered. These polynomials fullfill linear differential equation with some polynomial coefficients in their holonomic form. The aim of…

We consider orthogonal polynomials on the unit circle with respect to a weight which is a quotient of $q$-gamma functions. We show that the Verblunsky coefficients of these polynomials satisfy discrete Painlev\'e equations, in a Lax form,…

We investigate a class of power series occurring in some problems in quantum optics. Their coefficients are either Gegenbauer or Laguerre polynomials multiplied by binomial coefficients. Although their sums have been known for a long time,…

Let $(M,g)$ be a pseudo-Riemannian manifold and $F_\lambda(M)$ the space of densities of degree $\lambda$ on $M$. We study the space $D^2_{\lambda,\mu}(M)$ of second-order differential operators from $F_\lambda(M)$ to $F_\mu(M)$. If $(M,g)$…

Orthogonal polynomials and expansions are studied for the weight function $h_\kappa^2(x) \|x\|^{2\nu} (1-\|x\|^2)^{\mu-1/2}$ on the unit ball of $\mathbb{R}^d$, where $h_\kappa$ is a reflection invariant function, and for related weight…

We are concerned with the monic orthogonal polynomials with respect to a singularly perturbed Laguerre-type weight. By using the ladder operator approach, we derive a complicated system of nonlinear second-order difference equations…

Over an arbitrary field, we conduct a comprehensive study of the polynomial identities and codimensions of two- and three-dimensional metabelian non-Lie Leibniz algebras. In addition, we compute the images of multihomogeneous polynomials on…

We recall first some basic facts on weighted homogeneous functions and filtrations in the ring $A$ of formal power series. We introduce next their analogues for weighted homogeneous diffeomorphisms and vector fields. We show that the Milnor…

We consider a polynomial $P\in \mathbb{R}[x_{1},\cdots, x_{d}]$ of degree $ \delta $ that depends non-trivially on each of $x_1,...,x_d$ with $d\geq 2$. For any integer $t$ with $2\leq t\leq d$, any natural number $n \in \mathbb{N}$, and…

We describe bivariate polynomial sequences orthogonal to a symmetric weight function in terms of several bivariate polynomial sequences orthogonal with respect to Christoffel transformations of the initial weight under a quadratic…

We study the dependence of recurrence coefficients in the three-term recurrence relation for orthogonal polynomials with a certain deformation of the $q$-Laguerre weight on the degree parameter $n$. We show that this dependence is described…

In this paper we prove some characterizations of the matrix orthogonal polynomials whose derivatives are also orthogonal, which generalize other known ones in the scalar case. In particular, we prove that the corresponding orthogonality…

Let $f_k$ be the $k$-th Fourier coefficient of a function $f$ in terms of the orthonormal Hermite, Laguerre or Jacobi polynomials. We give necessary and sufficient conditions on $f$ for the inequality $\sum_{k}|f_k|^2\theta^k<\infty$ to…

We consider bivariate polynomials orthogonal on the bicircle with respect to a positive linear functional. The lexicographical and reverse lexicographical orderings are used to order the monomials. Recurrence formulas are derived between…

We present an explicit formula for the orthogonal projection onto the subspace of analytic polynomials of degree at most $n$ in the local Dirichlet space $D_\mu$ , where the positive measure $\mu$ consists of a finite number of Dirac…