ON SOME COMBINATIONS OF SELF-RECIPROCAL POLYNOMIALS

Title & Authors
ON SOME COMBINATIONS OF SELF-RECIPROCAL POLYNOMIALS
Kim, Seon-Hong;

Abstract
Let $\small{\mathcal{P}_n}$ be the set of all monic integral self-reciprocal poly-nomials of degree n whose all zeros lie on the unit circle. In this paper we study the following question: For P(z), Q(z)$\small{{\in}\mathcal{P}_n}$, does there exist a continuous mapping $\small{r{\rightarrow}G_r(z){\in}\mathcal{P}_n}$ on [0, 1] such that $\small{G_0}$(z) = P(z) and $\small{G_1}$(z) = Q(z)?.
Keywords
convex combination;polynomials;self-reciprocal polynomials;unit circle;zeros;
Language
English
Cited by
References
1.
H. J. Fell, On the zeros of convex combinations of polynomials, Pacific J. Math. 89 (1980), no. 1, 43-50.

2.
S. H. Kim, The zeros of certain family of self-reciprocal polynomials, Bull. Korean Math. Soc. 44 (2007), no. 3, 461-473.

3.
T. Sheil-Small, Complex Polynomials, Cambridge Studies in Advanced Mathematics 75, Cambridge University Press, Cambridge, 2002.