Functions with given moments and weight functions for orthogonal polynomials
type: Item
instance of: scholarly article
title: Functions with given moments and weight functions for orthogonal polynomials
zbMATH Open document ID: 0777.44003
author: A. J. Durán
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-08-17T00:00:00Z
review text: The author gives a constructive technique to find smooth functions with given moments. Earlier in the well-known moment problem it was guaranteed that for every sequence of complex numbers there is a function of bounded variation with the given moments in these numbers. The author shows how these weight functions are found. He uses the technique of Fourier and Hankel transform in Schwartz spaces to establish the respective functions with the given moments. Namely, he finds the functions for the classical orthogonal polynomials: the Bessel polynomials, the Hermite polynomials, the Laguerre and generalized Laguerre polynomials, and the Jacobi polynomials.
Mathematics Subject Classification ID: 44A60
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 218634
zbMATH Keywords: Fourier transform
zbMATH Keywords: moments
zbMATH Keywords: Hankel transform
zbMATH Keywords: Schwartz spaces
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: Bessel polynomials
zbMATH Keywords: Hermite polynomials
zbMATH Keywords: Laguerre polynomials
zbMATH Keywords: Jacobi polynomials
reviewed by: S. Yakubovich
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072612
OpenAlex ID: W1979804122
cites work: Q3728637
cites work: The Stieltjes moment problem for functions of bounded variation
cites work: The Stieltjes Moments Problem for Rapidly Decreasing Functions
cites work: On Hankel Transform
cites work: The Stieltjes Moment Problem with Complex Exponents
cites work: The Analytic Functionals in the Lower Half Plane as a Gel'fand-Shilov Space
cites work: Laguerre expansions of tempered distributions and generalized functions
cites work: Trajectory spaces, generalized functions and unbounded operators
cites work: Q5827353
cites work: Hyperfunctional weights for orthogonal polynomials
cites work: A New Class of Orthogonal Polynomials: The Bessel Polynomials
cites work: Orthogonal polynomials and singular Sturm-Liouville systems. I
cites work: Distributional Weight Functions for Orthogonal Polynomials
cites work: Q5771517
cites work: Q5571178
DOI: 10.1216/RMJM/1181072612
description: scientific article; zbMATH DE number 218634