On the spans of polynomials and their derivatives
Copyright policy )On the spans of polynomials and their derivatives
The main result of this paper is that if the set of zeroes of a polynomial is majorized by the set of the sums of zeroes of two other polynomials then the same relation is true for any derivative of these polynomials. This theorem is a nontrivial and very interesting generalization of the result of \textit{J. Borcea} and \textit{B. Shapiro} [C. R., Math., Acad. Sci. Paris 337, No.~11, 693--698 (2003; Zbl 1035.47022)]. It is shown in the paper that using this new result the classical theorem of J. Sz.-Nagy for the relation between the spans of a hyperbolic polynomial and its first derivative can be proved in a very easy fashion.
- University of Saskatchewan Canada
zeros of polynomials, Applied Mathematics, interlacing polynomials, majorization order, Polynomials in real and complex fields: location of zeros (algebraic theorems), Majorization order, Interlacing, Differentiators, Real polynomials: location of zeros, Spans of polynomials, Geometry of polynomials, Real algebraic sets, differentiators, spans of polynomials, Analysis
zeros of polynomials, Applied Mathematics, interlacing polynomials, majorization order, Polynomials in real and complex fields: location of zeros (algebraic theorems), Majorization order, Interlacing, Differentiators, Real polynomials: location of zeros, Spans of polynomials, Geometry of polynomials, Real algebraic sets, differentiators, spans of polynomials, Analysis
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