Year: 2015
Type: article
Abstract: Laguerre's theorem regarding the number of nonreal zeros of a polynomial and its image under certain linear operators is generalized.This generalization is then used to (1) exhibit a number of previously undiscovered complex zero decreasing sequences for the Jacobi, ultraspherical, Legendre, Chebyshev, and generalized Laguerre polynomial bases and (2) simultaneously generate a basis B and a corresponding complex zero decreasing sequence for the basis B. An extension to transcendental entire functions in the Laguerre-Pólya class is given, which, in turn, gives a new and short proof of a previously known result due to Piotrowski.The paper concludes with several open questions.
Source: Involve a Journal of Mathematics
Authors: Andre Bunton, Nicole Jacobs, Samantha Jenkins, Charles McKenry, Andrzej Piotrowski, Louis Scott
Institution: University of Alaska Southeast
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W1973034467