ON SOME COMBINATIONS OF SELF-RECIPROCAL POLYNOMIALS

Abstract

Let <TEX>$\mathcal{P}_n$</TEX> 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)<TEX>${\in}\mathcal{P}_n$</TEX>, does there exist a continuous mapping <TEX>$r{\rightarrow}G_r(z){\in}\mathcal{P}_n$</TEX> on [0, 1] such that <TEX>$G_0$</TEX>(z) = P(z) and <TEX>$G_1$</TEX>(z) = Q(z)?.