On polynomials with positive coefficients
The authors consider Lorentz polynomials with either non-negative or non- positive coefficients. Due to the non-uniqueness of representation in this class, the concept of the Lorentz degree is introduced and studied. Several theorems are proved concerning the Lorentz degree and the growth of Lorentz polynomials. For example, an estimate of the maximal Lorentz degree of all Lorentz polynomials with either non-negative or non- positive coefficients having no zeros in a certain open region in the complex plane containing (-1,1) is given. This is used to establish the (known) characterization that a polynomial not identically zero is a Lorentz polynomial with either non-negative or non-positive coefficients iff it has no roots in (-1,1).
scientific article; zbMATH DE number 4065579