Related papers: The Kontorovich-Lebedev transform as a map between…

We consider the transformation $\ev$ which associates to any element in a K-algebra A a function on the the set of its K-points. This is the analogue of the fundamental Gelfand transform. Both $\ev$ and its dual $\ev^*$ are the maps from a…

We show that the formalism of hybrid polynomials, interpolating between Hermite and Laguerre polynomials, is very useful in the study of Motzkin numbers and central trinomial coefficients. These sequences are identified as special values of…

The aim of this paper is to construct sup-exponentially localized kernels and frames in the context of classical orthogonal expansions, namely, expansions in Jacobi polynomials, spherical harmonics, orthogonal polynomials on the ball and…

Given a (not necessarily regular) holonomic D-module defined on the product of two complex manifolds, we prove that the associated correspondence commutes (in some sense) with the De Rham functor. We apply this result to the study of the…

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.

The aim of this paper is twofold. The first part is concerned with the associated and the so-called co-polynomials, i.e. new sequences obtained when finite perturbations of the recurrence coefficients are considered. In the second part we…

In this paper we study the following hypergeometric polynomials: $\mathcal{P}_n(x) = \mathcal{P}_n(x;\alpha,\beta,\delta_1,\dots,\delta_\rho,\kappa_1,\dots,\kappa_\rho) = {}_{\rho+2} F_{\rho+1}…

We derive a system of difference equations satisfied by the three-term recurrence coefficients of some families of discrete orthogonal polynomials.

We carry out some algebraic and analytic properties of a new class of orthogonal polyanalytic polynomials, including their operational formulas, recurrence relations, generating functions, integral representations and different…

Recursive algebraic construction of two infinite families of polynomials in $n$ variables is proposed as a uniform method applicable to every semisimple Lie group of rank $n$. Its result recognizes Chebyshev polynomials of the first and…

The dual Hahn polynomials $\{u_i(x)\}_{i=0}^d$ are a family of discrete orthogonal polynomials involving two real parameters $r$ and $s$. Let $L,L^*$ denote the corresponding Leonard pair. Assume that $r\not=0$ and $r+s=0$. We show that…

We study a q-generalization of the classical Laguerre/Hermite orthogonal polynomials. Explicit results include: the recursive coefficients, matrix elements of generators for the Heisenberg algebra, and the Hankel determinants. The power of…

We consider orthogonal polynomials on the surface of a double cone or a hyperboloid of revolution, either finite or infinite in axis direction, and on the solid domain bounded by such a surface and, when the surface is finite, by…

In this paper, we introduce a Kantorovich version of the Bernstein-type logarithmic operators. The idea comes from the wide literature concerning exponential polynomials that preserve exponential functions: here, the exponential weights are…

The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…

We present a derivation of classical Hermite, Laguerre, and Jacobi orthogonal polynomials directly through the Gram-Schmidt orthogonization process. The derivation uses certain generalized Vandermonde determinants with entries defined by…

Given an orthogonal polynomial sequence on the real line, another sequence of polynomials can be found by composing these polynomials with a general M\"obius transformation. In this work, we study the properties of such M\"obius-transformed…

We construct double Grothendieck polynomials of classical types which are essentially equivalent to but simpler than the polynomials defined by A.N.Kirillov in arXiv:1504.01469 and identify them with the polynomials defined by T.Ikeda and…

Homogeneous Besov and Triebel-Lizorkin spaces associated with multi-dimensional Laguerre function expansions of Hermite type with index $\alpha \in [-1/2,\infty)^d\backslash (-1/2,1/2)^d$, $d\geq 1$, are defined and investigated. To achieve…

The generalized L'vov-Kaplansky conjecture states that for any finite-dimensional simple algebra $A$ the image of a multilinear polynomial on $A$ is a vector space. In this paper we prove it for the algebra of octonions $\mathbb{O}$ over a…