The Cauchy Exponential of Linear Functionals on the Linear Space of Polynomials

In this paper, we introduce the notion of the Cauchy exponential of a linear functional on the linear space of polynomials in one variable with real or complex coefficients using a functional equation by using the so-called moment equation. It seems that this notion hides several properties and resu...

Full description

Saved in:

Bibliographic Details
Published in:	Mathematics (Basel) Vol. 11; no. 8; p. 1895
Main Authors:	Marcellán, Francisco, Sfaxi, Ridha
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01-04-2023
Subjects:	cauchy exponential of linear functional cauchy power of linear functional Functional equations Mathematical research Mathematics orthogonal polynomial sequence Polynomials positive-definite linear functional regular linear functional weakly-regular linear functional Spain
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	In this paper, we introduce the notion of the Cauchy exponential of a linear functional on the linear space of polynomials in one variable with real or complex coefficients using a functional equation by using the so-called moment equation. It seems that this notion hides several properties and results. Our purpose is to explore some of these properties and to compute the Cauchy exponential of some special linear functionals. Finally, a new characterization of the positive-definiteness of a linear functional is given.
ISSN:	2227-7390 2227-7390
DOI:	10.3390/math11081895