Dedicated to Professor Alfredo Eisinberg on the Occasion of his 70th birthday Keywords: Polynomial approximation L 2-norm Hilbert matrix Laguerre polynomials Bernstein polynomials a b s t r a c t The aim of this paper is to present a new approach to the finite time L 2-norm polynomial approximation problem. A new formulation of this problem leads to an equivalent linear system whose solution ca...

Relation between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), is well known. We use this relation to study the monotonicity properties of the zeros of generalized orthogonal polynomials. As examples, the Jacobi, Laguerre and Charlier polynomials are considered.  2005 Elsevier Inc. All...

Polynomial frames based on orthogonal decompositions with respect to weights of Laguerre and Hermite type are considered. Asymptotic formulas for the coefficients from expansions on such frames are presented. The ability to detect singularities of all order is studied in detail.

The purpose of this paper is to investigate the real sequences γ0, γ1, γ2, . . . with the property that if p(x) = ∑n k=0 akx k is any real polynomial, then ∑n k=0 γkakx k has no more nonreal zeros than p(x). In particular, the authors establish a converse to a classical theorem of Laguerre.

The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational methods, but in this paper, we investigate them techniques. By leveraging properties of Pascal functionals and Wronskian matrices, derive several identities for these polynomials, including recurrence relations. It is highlighted that identities, acquired via techniques, are distinct from the ones obta...

A novel generalized Gamma-Laguerre polynomial chaos expansion is proposed to account for the effect of random variations in lower bounded design parameters on antenna performance. After fitting a shifted Gamma distribution datasets such variables, predistorted generated based set orthogonal Laguerre polynomials. The new statistical methodology applied assess change resonance frequency when bend...

Some monotonicity results for the function f( )x ) n;k , where x ( ) n;k is the kth zero of generalized Laguerre polynomial L ) n (x) and f( ) is a suitable function of , are derived by means of the classical method of Stiltjes. c © 2002 Published by Elsevier Science B.V.

Given a stochastic process X = {Xt, t ∈ R+} with finite moments of convenient order, a time–space harmonic polynomial relative to X is a polynomial Q(x, t) such that the process Mt =Q(Xt, t) is a martingale with respect to the filtration associated with X . Major examples are the Hermite polynomials relative to a Brownian motion, the Charlier polynomials relative to a Poisson process and the La...

Let f be a real entire function with finitely many non-real zeros, not of the form f = Ph with P a polynomial and h in the Laguerre-Pólya class. Lower bounds are given for the number of non-real zeros of f ′′ + ωf , where ω is a positive real constant.