논문KCI 등재
ON SOME COMBINATIONS OF SELF-RECIPROCAL POLYNOMIALS
대한수학회 (The Korean Mathematical Society)|2012.01|대한수학회논문집 (Communications of the KMS)|제27권 제1호|pp. 175-183
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Let $\mathcal{P}_n$ 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)${\in}\mathcal{P}_n$, 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 G1(z) = Q(z)?.
Abstract
Let $\mathcal{P}_n$ 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)${\in}\mathcal{P}_n$, 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 G1(z) = Q(z)?.
참고문헌 (3)
- H. J. Fell, "On the zeros of convex combinations of polynomials", Pacic J. Math, 89(1), pp.43~50 (1980)
- 김선홍, "The zeros of certain family of self-reciprocal polynomials", 대한수학회보, 44(3), pp.461~473 (2007), 대한수학회
- T. Sheil-Small, "Complex Polynomials, In Cambridge Studies in Advanced Mathematics" (2002), Cambridge University Press
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