대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권1호
  • /
  • Pages.175-183
  • /
  • 2012
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON SOME COMBINATIONS OF SELF-RECIPROCAL POLYNOMIALS

  • 투고 : 2010.10.15
  • 발행 : 2012.01.31
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초록

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 $G_1$(z) = Q(z)?.

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참고문헌

  1. H. J. Fell, On the zeros of convex combinations of polynomials, Pacific J. Math. 89 (1980), no. 1, 43-50. https://doi.org/10.2140/pjm.1980.89.43
  2. S. H. Kim, The zeros of certain family of self-reciprocal polynomials, Bull. Korean Math. Soc. 44 (2007), no. 3, 461-473. https://doi.org/10.4134/BKMS.2007.44.3.461
  3. T. Sheil-Small, Complex Polynomials, Cambridge Studies in Advanced Mathematics 75, Cambridge University Press, Cambridge, 2002.