On some combinations of self-reciprocal polynomials
Commun. Korean Math. Soc. 2012 Vol. 27, No. 1, 175-183
Printed March 1, 2012
Seon-Hong Kim
Sookmyung Women's University
Abstract : Let $\mathcal P_n$ be the set of all monic integral self-reciprocal polynomials of degree $n$ whose all zeros lie on the unit circle. In this paper we study the following question: For $P(z)$, $Q(z) \in \mathcal P_n$, does there exist a continuous mapping $r \rightarrow G_r(z)\in \mathcal P_n$ on $[0,1]$ such that $G_0(z)=P(z)$ and $G_1(z)=Q(z)$?
Keywords : convex combination, polynomials, self-reciprocal polynomials, unit circle, zeros
MSC numbers : Primary 30C15; Secondary 26C10
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