Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE MAXIMUM AND MINIMUM MODULUS OF POLYNOMIALS ON CIRCLES

  • Received : 2017.12.04
  • Accepted : 2018.08.27
  • Published : 2018.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we consider both maximum modulus and minimum modulus on a circle of some polynomials. These give rise to interesting examples that are about moduli of Chebyshev polynomials and certain sums of polynomials on a circle. Moreover, we obtain some root locations of difference quotients of Chebyshev polynomials.

Keywords

References

  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. N. K. Govil, On the maximum modulus of polynomials, J. Math. Anal. Appl. 112 (1985), no. 1, 253-258. https://doi.org/10.1016/0022-247X(85)90289-6
  3. S.-H. Kim, Sums of two polynomials with each having real zeros symmetric with the other, Proc. Indian Acad. Sci. Math. Sci. 112 (2002), no. 2, 283-288. https://doi.org/10.1007/BF02829753
  4. S.-H. Kim and J. H. Lee, On difference quotients of Chebyshev polynomials, Bull. Korean Math. Soc. 53 (2016), no. 2, 373-386. https://doi.org/10.4134/BKMS.2016.53.2.373
  5. M. A. Qazi, On the maximum modulus of polynomials, Proc. Amer. Math. Soc. 115 (1992), no. 2, 337-343. https://doi.org/10.1090/S0002-9939-1992-1113648-1
  6. Q. I. Rahman and G. Schmeisser, Analytic Theory of Polynomials, London Mathematical Society Monographs. New Series, 26, The Clarendon Press, Oxford University Press, Oxford, 2002.
  7. T. J. Rivlin, On the maximum modulus of polynomials, Amer. Math. Monthly 67 (1960), 251-253. https://doi.org/10.2307/2309686