Related papers: Hermite subdivision schemes, exponential polynomia…
We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and…
In this paper we study the connection between the spectral condition of an Hermite subdivision operator and polynomial reproduction properties of the associated subdivision scheme. While it is known that in general the spectral condition…
Hermite subdivision schemes act on vector valued data that is not only considered as functions values in $\mathbb{R}^r$, but as consecutive derivatives, which leads to a mild form of level dependence of the scheme. Previously, we have…
We present an accurate investigation of the algebraic conditions that the symbols of a univariate, binary, Hermite subdivision scheme have to fulfil in order to reproduce polynomials. These conditions are sufficient for the scheme to…
Hermite interpolation property is desired in applied and computational mathematics. Hermite and vector subdivision schemes are of interest in CAGD for generating subdivision curves and in computational mathematics for building Hermite…
This work continues the research of generalized Heisenberg algebras connected with several orthogonal polynomial systems. The realization of the annihilation operator of the algebra corresponding to a polynomial system by a differential…
The aim of the paper is to present Hermite-type multiwavelets satisfying the vanishing moment property with respect to elements in the space spanned by exponentials and polynomials. Such functions satisfy a two-scale relation which is…
Motivated by classical results of approximation theory, we define an Hermite-type interpolation in terms of $n$-dimensional subspaces of the space of $n$ times continuously differentiable functions. In the main result of this paper, we…
This work is concerned with spectral collocation methods for fractional PDEs in unbounded domains. The method consists of expanding the solution with proper global basis functions and imposing collocation conditions on the Gauss-Hermite…
In this paper we present a factorization framework for Hermite subdivision schemes refining function values and first derivatives, which satisfy a spectral condition of high order. In particular we show that spectral order $d$ allows for…
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…
We study the case of Hermite subdivision operators satisfying a spectral condition of order greater than their size. We show that this can be characterized by operator factorizations involving Taylor operators and difference factorizations…
The bispectral anti-isomorphism is applied to differential operators involving elements of the stabilizer ring to produce explicit formulas for all difference operators having any of the Hermite exceptional orthogonal polynomials as…
The operational calculus associated with special polynomials has proven to be a powerful tool for analyzing and simplifying their properties. This article examines the bivariate degenerate Hermite polynomials with a focus on their…
We provide an explicit formula for the coefficient polynomials of a Hermite diagonal differential operator. The analysis of the zeros of these coefficient polynomials yields the characterization of generalized Hermite multiplier sequences…
In this work, based on quantum operator Hermite polynomials and Weyl's mapping rule, we find a generation function of the two-variable Hermite polynomials. And then, noting that the Weyl ordering is invariant under the similar…
In this paper, we consider linear differential equations satisfied by the generating function for Hermite polynomials and derive some new identities involving those polynomials.
We describe symmetric diffusion operators where the spectral decomposition is given through a family of orthogonal polynomials. In dimension one, this reduces to the case of Hermite, Laguerre and Jacobi polynomials. In higher dimension,…
Hermite spectral method plays an important role in the numerical simulation of various partial differential equations (PDEs) on unbounded domains. In this work, we study the superconvergence properties of Hermite spectral interpolation,…
Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for geometrically modeling curves/surfaces in CAGD and for building Hermite wavelets in numerical…