Related papers: Complex Hermite functions as Fourier-Wigner transf…
We develop a new method of umbral nature to treat blocks of Hermite and of Hermite like polynomials as independent algebraic quantities. The Calculus we propose allows the formulation of a number of practical rules allowing significant…
The continuous big $q$-Hermite polynomials are shown to realize a basis for a representation space of an extended $q$-oscillator algebra. An expansion formula is algebraically derived using this model.
In this paper we continue the discussion about relations between exponential polynomials and generalized moment generating functions on a commutative hypergroup. We are interested in the following problem: is it true that every finite…
We investigate a type of Hermite orthogonal polynomials on $r$ lines in the plane which have a common point at the origin and endpoints at the $r$ roots of unity and we show that their related Hermite functions are eigenfunctions of a…
We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates 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…
We consider a class of domains, generalizing the upper half-plane, and admitting rotational, translational and scaling symmetries, analogous to the half-plane. We prove Paley-Wiener type representations of functions in Bergman spaces of…
We provide transformation matrices for arbitrary Lorentz transformations of multidimensional Hermite functions in any dimension. These serve as a valuable tool for analyzing spacetime properties of MHS fields, and aid in the description of…
Let F(R^n) be the algebra of Fourier transforms of functions from L_1(R^n), K(R^n) be the algebra of Fourier transforms of bounded complex Borel measures in R^n and W be Wiener algebra of continuous 2pi-periodic functions with absolutely…
A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with the help of a family of weight functions is considered in this paper. For…
We establish identities for the composition $T_{k,n}(|\widehat{gd\sigma}|^2)$, where $g\mapsto \widehat{gd\sigma}$ is the Fourier extension operator associated with a general smooth $k$-dimensional submanifold of $\mathbb{R}^n$, and…
This paper describes an extension of Fourier approximation methods for multivariate functions defined on the torus $\mathbb{T}^d$ to functions in a weighted Hilbert space $L_{2}(\mathbb{R}^d, \omega)$ via a multivariate change of variables…
In a previous paper we deformed Hermite polynomials to three associated polynomials .Here we apply the same deformation to Laguerre polynomials .
The aim of this paper is to construct generating functions for new families of special polynomials including the Appel polynomials, the Hermite-Kamp\`e de F\`eriet polynomials, the Milne-Thomson type polynomials, parametric kinds of Apostol…
We introduce a new family of hyperplane arrangements inspired by the homogenized Linial arrangement (which was recently introduced by Hetyei), and show that the intersection lattices of these arrangements are isomorphic to the bond lattices…
We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of $\mathscr{L}_2(\mathbb{R})$. This allows us to derive explicit expansions on the real…
Let (G, V) be a prehomogeneous vector space, let O be any G(F_q)-invariant subset of V(F_q), and let f be the characteristic function of O. In this paper we develop a method for explicitly and efficiently evaluating the Fourier transform of…
For the TZ metric on the moduli space $\mathscr{M}_{0,n}$ of $n$-pointed rational curves, we construct a K\"ahler potential in terms of the Fourier coefficients of the Klein's Hauptmodul. We define the space $\mathfrak{S}_{g,n}$ as…
We provide an algebraic interpretation for two classes of continuous $q$-polynomials. Rogers' continuous $q$-Hermite polynomials and continuous $q$-ultraspherical polynomials are shown to realize, respectively, bases for representation…
We prove a generalization of the Kibble--Slepian formula (for Hermite polynomials) and its unitary analogue involving the $2$D Hermite polynomials recently proved in \cite{Ism4}. We derive integral representations for the $2$D Hermite…