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Remarks on the Gauss-Lucas theorem in higher dimensional space


Author: A. W. Goodman
Journal: Proc. Amer. Math. Soc. 55 (1976), 97-102
MSC: Primary 30A08; Secondary 26A78
DOI: https://doi.org/10.1090/S0002-9939-1976-0435366-6
MathSciNet review: 0435366
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Abstract: A recent paper by J. B. Diaz and Dorothy Browne Shaffer extends the Gauss-Lucas Theorem to $ n$-dimensional Euclidean space. The authors leave open certain natural questions concerning the existence of ``zeros of the derivative". This paper answers three such questions, and suggests several other questions for further investigation.


References [Enhancements On Off] (What's this?)

  • [1] J. B. Diaz and Dorothy Browne Shaffer, A generalization to higher dimensions of a theorem of Lucas concerning the zeros of the derivative of a polynomial of one complex variable, Proc. Internat. Congress Math. (Vancouver, 1974), Canad. Math. Congress (to appear). MR 0435365 (55:8325)
  • [2] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR22 #8302. MR 0117523 (22:8302)
  • [3] Morris Marden, Geometry of polynomials, Math. Surveys, no. 3, Amer. Math. Soc., Providence, R.I., 1966. MR27 #1562. MR 0225972 (37:1562)
  • [4] G.V. Sz.-Nagy, Über die Lage der Nullstellen eines Abstandspolynoms and seiner Derivierten, Bull. Amer. Math. Soc. 55(1949), 329-342. MR10, 702. MR 0030036 (10:702g)
  • [5] A. Schurrer, On the location of the zeros of the derivative of rational functions of distance polynomials, Trans. Amer. Math. Soc. 89(1958), 100-112. MR20 #4634. MR 0098172 (20:4634)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0435366-6
Keywords: Polynomials, zeros of the derivative, Euclidean $ n$-space, gradient, Gauss-Lucas Theorem
Article copyright: © Copyright 1976 American Mathematical Society

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