The Cauchy Exponential of Linear Functionals on the Linear Space of Polynomials Articles uri icon

publication date

  • April 2023

start page

  • 1

end page

  • 18

issue

  • 8

volume

  • 11

International Standard Serial Number (ISSN)

  • 2227-7390

abstract

  • 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.

subjects

  • Mathematics

keywords

  • cauchy exponential of linear functional; cauchy power of linear functional; du-laguerre-hahn operator; orthogonal polynomial sequence; positive-definite linear functional; regular linear functional; weakly-regular linear functional